Books, Book Chapters, & Research Papers

In the ever-evolving landscape of research, the synergy between mathematics, machine learning, and various application domains has yielded groundbreaking insights and transformative solutions. This interdisciplinary approach harnesses the power of mathematical modeling and machine learning algorithms to address complex challenges in diverse fields such as finance, healthcare, climate science, and beyond. Whether optimizing financial portfolios, predicting disease outbreaks, or understanding climate patterns, the fusion of mathematics and machine learning enhances our ability to extract meaningful patterns and make informed decisions. To delve into our latest research endeavors at the intersection of mathematics, machine learning, and diverse applications, explore our publications on Google Scholar and arXiv. Join us in the exploration of innovative solutions that emerge from the convergence of these dynamic disciplines.

PUBLICATION LIST

(* indicates a PhD student supervised by George Em. Karniadakis)

A1. Books:

  1. M. Zayernouri*, L. Wang, J. Shen and G.E. Karniadakis,” Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations,” Cambridge University Press, 2024.
  2. Z. Zhang* and G.E. Karniadakis, “Numerical Methods for Stochastic PDEs with White Noise,” Springer, Applied Mathematics Series, 2017.
  3. G.E. Karniadakis, A. Beskok* and N. Aluru, “Microflows and Nanoflows: Fundamentals and Simulation,” Springer 2005.
  4. G.E. Karniadakis and R.M. Kirby*, “Parallel Scientific Computing in C++ and MPI,” Cambridge University Press, March 2003.
  5. G.E. Karniadakis and A. Beskok*, “Microflows: Fundamentals and Simulation,” Springer, 2001. (first textbook/monograph in this field).
  6. G.E. Karniadakis S.J. Sherwin*, “Spectral/hp Element Methods for CFD,” Oxford University Press, New York, 1999. (first monograph in this field); second edition, Oxford, 2005; third edition, 2013.

A2. Chapters in Books/Special Issues

  1. G. Pang, G. E. Karniadakis, “Physics-Informed Learning Machines for Partial Differential Equations: Gaussian Processes Versus Neural Networks Springer,” Emerging Frontiers in Nonlinear Science pp 323-343, https://doi.org/10.1007/978, May 2020.
  2. Handbook of Fractional Calculus with Applications, vol. 3, Numerical Methods, Editor G.E, Karniadakis, De Guyter, 2019.
  3. WK Liu, G Karniadakis, S Tang, J Yvonnet, “A Computational Mechanics Special Issue on: Data- Driven Modeling and Simulation-theory, Methods, and Applications,” Computational Mechanics 64 (2), 279-279, 2019.
  4. Y. Yu, R.M. Kirby, G.E. Karniadakis, “Spectral Element and hp Methods,” Encyclopedia of Computational Mechanics Second Edition, 1-43.
  5. Z. Li, X. Bian, X.J. Li, M.G. Deng, Y.H. Tang, B. Caswell and G.E. Karniadakis, “Dissipative Particle Dynamics: Foundation, Implementation and Applications,” In book: Particles in Flows, Editor: T. Bodn´ar, G.P. Galdi and Sˇ. Neˇcasov´a, Birkh¨auser, Cham, 2017.
  6. L. Xuejin, L. Zhen, X. Bian, M. Deng, C. Kim, Y. Tang*, A. Yazdani, G.E. Karniadakis, “Dissipative Particle Dynamics, Overview,” Encyclopedia of Nanotechnology, 2016.
  7. G.E. Karniadakis, J.S. Hesthaven, I. Podlubny, Special Issue on “Fractional PDEs: Theory, Numerics, and Applications,” J. Comput. Phys. 293, 1-3, 2015.
  8. L. Grinberg*, M. Deng, A. Yakhot and G.E. Karniadakis, “Window Proper Orthogonal Decomposition: Application to Continuum and Atomistic Data,” Reduced Order Methods for Modeling and Computational Reduction, Springer, vol. 9, eds. A. Quarteroni and G. Rozza, p. 275, 2014.
  9. D.A. Fedosov, I.V. Pivkin, W. Pan, M. Dao, B. Caswell and G.E., Karniadakis, “Multiscale Modeling of Hematologic Disorders,” in Modeling of Physiological Flows edited by D. Ambrosi, A. Quarteroni and G. Rozza, Springer, Milan, Italy, 2011.
  10. I.V. Pivkin*, B. Caswell and G.E. Karniadakis, “Dissipative Particle Dynamics,” Chapter 2 in Reviews in Computational Chemistry, Vol. 27, edited by Kenny B. Lipkowitz, John Wiley Sons, Inc., 2011.
  11. D.A. Fedosov*, B. Caswell and G.E., Karniadakis, “Dissipative Particle Dynamics Modeling of Red Blood Cells,” in Computational Hydrodynamics of Capsules and Biological Cells, edited by C. Pozrikidis, CRC Press, Boca Raton, FL, 2010.
  12. N. Aluru and G.E. Karniadakis, “Numerical Simulation of Microflows and Nanoflows,” Chapter 3 in Micro/Nano Technology Systems for Biomedical Applications, edited by C.-M. Ho, Oxford University Press, 2010.
  13. X. Wan and G.E. Karniadakis, “Adaptive Numerical Solutions of Stochastic Differential Equations,” Computer Mathematics and its Applications (1994-2005), pp. 561-573, 2006.
  14. “Spectral Interpolation in Non-Orthogonal Domains: Algorithms and Applications,” special issue of Journal of Engineering Mathematics, guest editor (co-editor: Jan Hesthaven).
  15. “Uncertainty Quantification in Simulation Science,” special issue of Journal of Computational Physics, vol. 217, no. 1, 2006, guest editor (co-editor: James Glimm).
  16. V Symeonidis*, GE Karniadakis and B Caswell, “Simulation of Phage DNA in Microchannels Using Dissipative Particle Dynamics,” Bulletin of the Polish Academy of Sciences, vol. 53 (4), pp. 395-403, 2005.
  17. D. Xiu* and G.E. Karniadakis, “Generalized Polynomial Chaos: Performance Evaluation and Applications,” chapter in Dynamic Data Driven Applications Simulations (DDDAS), editor F. Darema, Kluwer, 2004.
  18. R.M. Kirby* and G.E. Karniadakis, “Spectral Element and HP Methods,” Encyclopedia of Computational Mechanics, John Wiley Sons Ltd, 2004.
  19. G.E. Karniadakis and K.-S. Choi, “Mechanisms on Transverse Motions in Turbulent Wall Flows,” Annual Review of Fluid Mechanics, vol. 35, 45-62, 2003.
  20. G.E. Karniadakis, “Quantifying Uncertainty in CFD”, Managing Editor of special issue of J. Fluids Engineering, March 2002.
  21. R.M. Kirby* and G.E. Karniadakis, “Under-Resolution and Diagnostics in Turbulent Simulations of Complex-Geometry Flows,” Turbulent Flow Computations, Kluwer, 2002.
  22. R.M. Kirby*, G.E. Karniadakis, O. Mikulchenko and K. Mayaram, “Integrated Simulation for MEMS: Coupling Flow- Structure-Thermal-Electrical Domains,” Chapter 5, The MEMS Handbook, CRC Press.
  23. “Spectral, Spectral Element and HP Methods for CFD,” guest editor of C.M.A.M.E., (co-editors: M. Ainsworth and C. Bernardi), vol. 175.
  24. “Discontinuous Galerkin Methods: Theory Computation and Applications,” (editors: B. Cockburn, G.E. Karniadakis and C.-W. Shu), Springer-Verlag, February 2000.
  25. G.E. Karniadakis and R.D. Henderson*, “Spectral Element Methods for Incompressible Flows,” chapter 29 in Handbook of Fluid Dynamics, edited by R.W. Johnson, CRC Press, 1998.
  26. G.E. Karniadakis, “Towards a Numerical Error Bar in CFD,” Editorial Article, J. Fluids Engineering, March 1995.
  27. G.E. Karniadakis S.A. Orszag, “Nodes, Modes, and Flow Codes,” Physics Today, p. 34-42, March 1993.
  28. G.E. Karniadakis S.A. Orszag, “Some Novel Aspects of Spectral Methods,” Algorithmic Trends in Computational Fluid Dynamics,” eds. M.Y. Hussaini, A. Kumar, M.D. Salas, p. 245, Springer- Verlag, 1993.
  29. G.E. Karniadakis, S.A. Orszag, E.M. Ronquist and A.T. Patera, “Spectral Element and Lattice Gas Methods for Incompressible Fluid Dynamics,” chapter 8 in Incompressible Fluid Dynamics, eds. M.D. Gunzburger and R.A. Nicolaides, Cambridge University Press, 1993.
  30. R.D. Henderson* G.E. Karniadakis, “A Hybrid Spectral Element-finite Difference Method for Parallel Computers,” p. 221, Unstructured Scientific Computation on Scalable Multi-Processors, ed. P. Mehrotra, J. Saltz, and R. Voigt, M.I.T. Press, 1992.
  31. G.E. Karniadakis S.A. Orszag, “Parallel Spectral Computations of Complex Engineering Flows,” chapter 9 in Super-computing in Engineering Analysis, New Generation Computing, ed. H. Adeli, 1990.

B. Articles in Refereed Journals:
Machine and Deep Learning

  1. K Shukla, Z Zou, CH Chan, A Pandey, Z Wang, G Karniadakis, “NeuroSEM: A Hybrid Framework for Simulating Multiphysics Problems by Coupling PINNs and Spectral Elements,” Computer Methods in Applied Mechanics and Engineering 433, 117498.
  2. X Xou, X Meng, G Karniadakis, “Uncertainty Quantification for Noisy Inputs-Outputs in Physics-Informed Neural Networks and Neural Operators, “Computer Methods in Applied Mechanics and Engineering 433, 117498.
  3. Z Zou, T Meng, P Chen, J Darbone, G Karniadakis, “Leveraging Viscous Hamilton–Jacobi PDEs for Uncertainty Quantification in Scientific Machine Learning,” Society for Industrial and Applied Mathematics, 2024.
  4. S Mariappan, K Nath, G Karniadakis, “Learning Thermoacoustic Interactions in Combustors Using a Physics-Informed Neural Network,” Engineering Applications of Artificial Intelligence, 2024.
  5. F De Castro Teixeira Carvalho, K Nath, A Luiz Serpa, G Karniadakis, “Learning Characteristic Parameters and Dynamics of Centrifugal Pumps Under Multiphase Flow Using Physics-Informed Neural Networks,” Engineering Applications of Artificial Intelligence, 2024.
  6. Z Hu, NA Daryakenari, Q Shen, K Kawaguchi, G Karniadakis, “State-space models are accurate and efficient neural operators for dynamical systems,” arXiv preprint arXiv:2409.03231, 2024.
  7. M Raissi, P Perdikaris, N Ahmadi, G Karniadakis, “Physics-Informed Neural Networks and Extensions,” arXiv preprint arXiv:2408.16806, 2024.
  8. AJ Varghese, Z Zhang, G Karniadakis, “SympGNNs: Symplectic Graph Neural Networks for Identifiying High-Dimensional Hamiltonian Systems and Node Classification,” arXiv preprint arXiv:2408.16698, 2024.
  9. Q Zhang, A Kahana, G Karniadakis, P Stinis, “Sms: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations,” Journal of Computational Physics, 113363, 2024.
  10. M Lu, C Lin, M Maxey, G Karniadakis, Z Li, “Bridging Scales in Multiscale Bubble Growth Dynamics with Correlated Fluctuations Using Neural Operator Learning,” International Journal of Multiphase Flow,” International Journal of Multiphase Flow, 104959, 2024.
  11. M De Florio, Z Zou, D Schiavazzi, G Karniadakis, “Quantification of Total Uncertainty in the Physics-informed Reconstruction of CVSim-6 Physiology,” arXiv:2408.07201v1, 2024.
  12. Z Zhang, C Wang, S Liu, J Darbon, G Karniadakis, “A Time-Dependent Symplectic Network for Non-Convex Path Planning Problems with Linear and Nonlinear Dynamics,” arXiv preprint arXiv:2408.03785, 2024.
  13. P Gao, G Karniadakis, P Stinis, “Multiscale Modeling Framework of a Constrained Fluid with Complex Boundaries Using Twin Neural Networks,” arXiv preprint arXiv:2408.03263, 2024.
  14. V Kumar, S Goswami, K Kontolati, MD Shields, G Karniadakis, “Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving,” arXiv preprint arXiv:2408.02198, 2024.
  15. O Ovadia, A Kahana, P Stinis, E Turkel, D Givoli, G Karniadakis, “Vito: Vision Transformer-operator,” Computer Methods in Applied Mechanics and Engineering, 428, 117109, 2024.
  16. Q Cao, S Goswami, G Karniadakis, “Laplace Neural Operator for Solving Differential Equations,” Nature Machine Intelligence, 1-10, 2024.
  17. Z Hu, K Shukla, G Karniadakis, K Kawaguchi, “Tackling the Curse of Dimensionality with Physics-informed Neural Networks,” Neural Networks, 106369, 2024.
  18. J Song, M Zhong, G Karniadakis, Z Yan, “Two-stage Initial-value Iterative Physics-informed Neural Networks for Simulating Solitary Waves of Nonlinear Wave Equations,” Journal of Computational Physics 505, 112917, 2024.
  19. Z Zou, X Meng, G Karniadakis, “Correcting Model Misspecification in Physics-informed Neural Networks (PINNs),” Journal of Computational Physics 505, 112918, 2024.
  20. Z Hu, Z Shi, G Karniadakis, K Kawaguchi, “Hutchinson Trace Estimation for High-dimensional and High-order Physics-informed Neural Networks,” Computer Methods in Applied Mechanics and Engineering 424, 116883, 2024.
  21. P Chen, T Meng, Z Zou, J Darbon, G Karniadakis, “Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems,” SIAM Journal on Scientific Computing 46 (2), C216-C248, 2024.
  22. AJ Varghese, A Bora, M Xu, G Karniadakis, “TransformerG2G: Adaptive Time-Stepping for Learning Temporal Graph Embeddings Using Transformers,” Neural Networks 172, 106086, 2024.
  23. SJ Anagnostopoulos, JD Toscano, N Stergiopulos, G Karniadakis, “Learning in PINNs: Phase Transition, Total Diffusion, and Generalization,” arXiv preprint arXiv:2403.18494, 2024.
  24. J Song, M Zhong, G Karniadakis, Z Yan, “Two-stage Initial-value Iterative Physics-informed Neural Networks for Simulating Solitary Waves of Nonlinear Wave Equations,” Journal of Computational Physics, 112917, 2024.
  25. N Ahmadi Daryakenari, M De Florio, K Shukla, G Karniadakis, “AI-Aristotle: A Physics-informed Framework for Systems Biology Gray-box Identification,” PLOS Computational Biology 20 (3), e1011916, 2024.
  26. Z Zou, X Meng, G Karniadakis, “Correcting Model Misspecification in Physics-informed Neural Networks (PINNs),” Journal of Computational Physics, 112918, 2024.
  27. SJ Anagnostopoulos, JD Toscano, N Stergiopulos, G Karniadakis, “Residual-based Attention in Physics-informed Neural Networks,” Computer Methods in Applied Mechanics and Engineering 421, 116805, 2024.
  28. K Shukla, V Oommen, A Peyvan, M Penwarden, N Plewacki, L Bravo, “Deep neural operators as accurate surrogates for shape optimization,” Engineering Applications of Artificial Intelligence 129, 107615, 2024.
  29. NA Daryakenari, M De Florio, K Shukla, G Karniadakis, “AI-Aristotle: A physics-informed framework for systems biology gray-box identification,” Plos Computational Biology 20, 2024.
  30. Q Zhuang, CZ Yao, Z Zhang, G Karniadakis, “Two-scale Neural Networks for Partial Differential Equations with Small Parameters,” arXiv preprint arXiv:2402.17232, 2024.
  31. E Haghighat, U bin Waheed, G Karniadakis, “En-DeepONet: An Enrichment Approach for Enhancing the Expressivity of Neural Operators with Applications to Seismology,” Computer Methods in Applied Mechanics and Engineering 420, 116681, 2024.
  32. Y Kim, A Kahana, R Yin, Y Li, P Stinis, GE Karniadakis, P Panda, “Rethinking Skip Connections in Spiking Neural Networks with Time-To-First-Spike Coding,” Frontiers in Neuroscience 18, 1346805, 2024.
  33. Z Hu, Z Zhang, GE Karniadakis, K Kawaguchi, “Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations,” arXiv preprint arXiv:2402.07465, 2024.
  34. Y Zhang, Y Qiang, H Li, G Li, L Lu, M Dao, GE Karniadakis, AS Popel, “Signaling-biophysical Modeling Unravels Mechanistic Control of Red Blood Cell Phagocytosis by Macrophages in Sickle Cell Disease,” …PNAS nexus 3 (2), pgae031, 2024.
  35. Z Zhang, Z Zou, E Kuhl, GE Karniadakis, “Discovering a Reaction–diffusion Model for Alzheimer’s Disease by Combining PINNs with Symbolic Regression,” Computer Methods in Applied Mechanics and Engineering 419, 116647, 2024.
  36. S Goswami, AD Jagtap, H Babaee, BT Susi, GE Karniadakis, “Learning Stiff Chemical Kinetics Using extended deep neural operators,” Computer Methods in Applied Mechanics and Engineering 419, 116674, 2024.
  37. A Peyvan, V Oommen, AD Jagtap, GE Karniadakis, “RiemannONets: Interpretable Neural Operators for Riemann Problems,” arXiv preprint arXiv:2401.08886, 2024.
  38. A Kopaničáková, GE Karniadakis, “Deeponet based preconditioning strategies for solving parametric linear systems of equations,” arXiv preprint arXiv:2401, 2024.
  39. AJ Varghese, A Bora, M Xu, GE Karniadakis, “TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers.” Neural Networks. 2024 Apr 1;172:106086.
  40. Anagnostopoulos SJ, Toscano JD, Stergiopulos N, Karniadakis GE. “Residual-based attention in physics-informed neural networks.” Computer Methods in Applied Mechanics and Engineering. 2024 Mar 1;421:116805.
  41. Borrel-Jensen N, Goswami S, Engsig-Karup AP, Karniadakis GE, Jeong CH. “Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators.” Proceedings of the National Academy of Sciences. 2024 Jan 9;121(2):e2312159120.
  42. Hu Z, Jagtap AD, Karniadakis GE, Kawaguchi K. “Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology.” Engineering Applications of Artificial Intelligence. 2023 Nov 1;126:107183.
  43. Lin C, Maxey M, Li Z, Karniadakis GE. “A seamless multiscale operator neural network for inferring bubble dynamics.” Journal of Fluid Mechanics. 2021 Dec;929.
  44. Lou Q, Meng X, Karniadakis GE. “Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation.” Journal of Computational Physics. 2021 Dec 15;447:110676.
  45. Mao Z, Lu L, Marxen O, Zaki TA, Karniadakis GE. “DeepMMnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators.” Journal of Computational Physics. 2021 Dec 15;447:110698.
  46. Jagtap AD, Shin Y, Kawaguchi K, Karniadakis GE. “Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions.” Neurocomputing. 2022 Jan 11;468:165-80.
  47. E. Kharazmi, M. Cai, Z. Zhang, G. Lin, and GE Karniadakis, “Identifiability and predictability of integer-and fractional-order epidemiological models using physics-informed neural networks”, Nat Comput Sci (2021). https://doi.org/10.1038/s43588-021-00158-0.
  48. L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis, ”DeepXDE: A Deep Learning Library for Solving Differential Equations,” SIAM Rev., 63(1), 208–228. (21 pages), DOI. 10.1137/19M1274067, February 2021.
  49. G.E. Karniadakis, I.G. Kevrekidis, L. Lu, et al., ”Physics-informed machine learning”, Nature Review Physics 3, 422–440 (2021), https://doi.org/10.1038/s42254-021-00314-5
  50. S. Cai, H. Li, F. Zheng, F. Kong, M. Dao, GE Karniadakis, Subra Suresh, ” Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease”, Proceedings of National Academy of Sciences, 118 (13) e2100697118; DOI: 10.1073/pnas.2100697118, Mar 2021.
  51. L. Yang, X. Meng, G. E. Karniadakis, “B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data”, Journal of Computational Physics, Volume 425, 109913, January 2021.
  52. X. Jin, S. Cai, H. Li, G. E. Karniadakis, “NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equation”, Journal of Computational Physics, Volume 426, 109951, February 2021.
  53. E. Kharazmi, Z. Zhang, G.E. Karniadakis, ”hp-VPINNs: Variational physics-informed neural networks with domain decomposition”, Computer Methods in Applied Mechanics and Engineering, Volume 374, 113547, February 2021.
  54. S. Cai, Z. Wang, F. Fuest, Y. Jeon, C. Gray, G. Karniadakis, “Flow over an espresso cup: Inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks”, Journal of Fluid Mechanics, 915, A102. doi:10.1017/jfm.2021.135, March 2021
  55. S Cai, Z Wang, L Lu, TA Zaki, GE Karniadakis, “DeepMMnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks,” Journal of Computational Physics, 110296, 2021.
  56. S Cai, Z Wang, S Wang, P Perdikaris, G Karniadakis, “Physics-Informed Neural Networks (PINNs) for Heat Transfer Problems,” Journal of Heat Transfer, 2021.
  57. M Mahmoudabadbozchelou, M Caggioni, S Shahsavari, WH Hartt, S Jamali, GE Karniadakis, “Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework,” Journal of Rheology 65 (2), 179-198, 201.
  58. L Lu, P Jin, G Pang, Z Zhang, GE Karniadakis, “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,” Nature Machine Intelligence 3 (3), 218-229, 2021.
  59. M Yin, X Zheng, JD Humphrey, GE Karniadakis, “Non-invasive inference of thrombus material properties with physics-informed neural networks,” Computer Methods in Applied Mechanics and Engineering 375, 113603, 2021.
  60. L Zhao, Z Li, Z Wang, B Caswell, J Ouyang, GE Karniadakis, “Active-and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows,” Journal of Computational Physics 427, 110069, 2021.
  61. J del A´guila Ferrandis, MS Triantafyllou, C Chryssostomidis, GE, Karniadakis, “Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states,” Proceedings of the Royal Society A 477 (2245), 20190897, 2021.
  62. L Lu, X Meng, Z Mao, GE Karniadakis, “DeepXDE: A deep learning library for solving differential equations,” SIAM Review 63 (1), 208-228, 2021.
  63. P Jin, Z Zhang, A Zhu, Y Tang, GE Karniadakis, “SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems,” Neural Networks 132, 166-179, 2020.
  64. A Yazdani, L Lu, M Raissi, GE Karniadakis, “Systems biology informed deep learning for inferring parameters and hidden dynamics,” PLoS computational biology 16 (11), e1007575, 2020.
  65. AD Jagtap, GE Karniadakis, “Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations,” Communications in Computational Physics 28 (5), 2002-2041, 2020.
  66. D Fan, L Yang, Z Wang, MS Triantafyllou, GE Karniadakis, “Reinforcement learning for bluff body active flow control in experiments and simulations,” Proceedings of the National Academy of Sciences 117 (42), 26091- 26098, 202.
  67. L. Yang and G.E. Karniadakis, “Potential Flow Generator with L2 optimal transport regularity for generative models,” IEEE Transactions on Neural Networks and Learning Systems,” doi: 10.1109- TNNLS.2020.3028042, 2020.
  68. L. Yang, X. Meng and G,.E. Karniadakis, “B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data,” Journal of Computational Physics, 109913, 2021.
  69. P. Jin, Z. Zhang, A. Zhu, Y. Tang, G.E. Karniadakis, “SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems,” Neural Networks, 132, pp.166-179, 2020.
  70. Q Zheng, L Zeng, GE Karniadakis, “Physics-informed semantic inpainting: Application to geostatistical modeling, Journal of Computational Physics,” 419, 10967, 2020.
  71. G. Pang, M. D’Elia, M. Parks, G. E. Karniadakis, “nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator.” Algorithms and applications, Journal of Computational Physics Volume 422, 109760, December 2020.
  72. K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, G. E. Karniadakis, “Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks,” Journal of Nondestructive Evaluation, Article number: 61, August 2020.
  73. A. D. Jagtap, K. Kawaguchi, G. E. Karniadakis, “Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks,” Proceedings of the Royal Society, https://doi.org/10.1098/rspa.2020.0334, July 2020.
  74. X. Meng, Z. Li, D. Zhang, G. E. Karniadakis, “PPINN: Parareal physics-informed neural network for time-dependent PDEs,” Computer Methods in Applied Mechanics and Engineering, Volume 370, https://doi.org/10.1016/j.cma.2020.113250, October 2020
  75. P.Jin, L. Lu, Y. Tanga, G. E. Karniadakis, “Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness,” Neural Networks, https://doi.org/10.1016/ j.neunet.2020.06.024, July 2020.
  76. Y. Chen, L. Lu, G. E. Karniadakis and L. D. Negro, “Physics-informed neural networks for inverse problems in nano-optics and metamaterials,” Optics Express, Vol. 28, Issue 8, pp. 11618-11633, https://doi.org/10.1364/OE.384875, 2020.
  77. Q Zheng, L Zeng, GE Karniadakis, “Physics-informed semantic inpainting: Application to geostatistical modeling,” Journal of Computational Physics, 109676, 2020.
  78. AD Jagtap, E Kharazmi, GE Karniadakis, “Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems,” Computer Methods in Applied Mechanics and Engineering 365, 113028, 2020.
  79. L Lu, M Dao, P Kumar, U Ramamurty, GE Karniadakis, S Suresh, “Extraction of mechanical properties of materials through deep learning from instrumented indentation,” Proceedings of the National Academy of Sciences, March 16, 2020.
  80. Z Mao, AD Jagtap, GE Karniadakis, “Physics-informed neural networks for high-speed flows,” Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020.
  81. AD Jagtap, K Kawaguchi, GE Karniadakis, “Adaptive activation functions accelerate convergence in deep and physics-informed neural networks,” Journal of Computational Physics 404, 109136, 2020.
  82. M Raissi, A Yazdani, GE Karniadakis, “Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations,” Science 367 (6481), 1026-1030, 2020.
  83. GCY Peng, M Alber, AB Tepole, WR Cannon, S De, ., GE Karniadakis, E. Kuhl, “Multiscale Modeling Meets Machine Learning: What Can We Learn?,” Archives of Computational Methods in Engineering, 1-2, 2020.
  84. X Meng, GE Karniadakis, “A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems,” Journal of Computational Physics 401, 109020, 2020.
  85. L Yang, D Zhang, GE Karniadakis, “Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations,” SIAM Journal on Scientific Computing 42 (1), A292-A317, 2020.
  86. D Zhang, L Guo, GE Karniadakis, “Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks,” SIAM Journal on Scientific Computing 42 (2), A639- A665, 2020.
  87. PP Mehta, G Pang, F Song, GE Karniadakis, “Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network,” Fractional Calculus and Applied Analysis 22 (6), 1675-1688, 2019.
  88. Z Mao, Z Li, GE Karniadakis, “Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations,” Communications on Applied Mathematics and Computation 1 (4), 597- 619, 2019.
  89. D Fan, G Jodin, TR Consi, L Bonfiglio, Y Ma, LR Keyes, GE Karniadakis, …,MS Triantafyllou, “A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics,” Science Robotics 4 (36), 2019.
  90. M Alber, AB Tepole, WR Cannon, S De, S Dura-Bernal, K Garikipati, …, GE Karniadakis, E. Kuhl, “Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences,” npj Digital Medicine 2 (1), 1-11, 2020.
  91. D Zhang, L Lu, L Guo, GE Karniadakis, “Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems,” Journal of Computational Physics, 2019.
  92. G Pang, L Lu, GE Karniadakis, “fPINNs: Fractional physics-informed neural networks,” SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019.
  93. M Raissi, H Babaee, GE Karniadakis, “Parametric Gaussian process regression for big data,” Computational Mechanics 64 (2), 409-41, 2019.
  94. M Gulian, M Raissi, P Perdikaris, G Karniadakis, “Machine learning of space-fractional differential equations,” SIAM Journal on Scientific Computing 41 (4), A2485-A2509, 2019.
  95. AL Blumers, Z Li, GE Karniadakis, “Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics,” Journal of Computational Physics 393, 214-228, 2019.
  96. G Pang, L Yang, GE Karniadakis, “Neural-net-induced Gaussian process regression for function approximation and PDE solution,” Journal of Computational Physics 384, 270-288, 2019.
  97. S Lee, F Dietrich, GE Karniadakis, IG Kevrekidis, “Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion,” Interface Focus 9 (3), 20180083, 2019.
  98. M Raissi, Z Wang, MS Triantafyllou, GE Karniadakis, “Deep learning of vortex-induced vibrations,” Journal of Fluid Mechanics 861, 119-137, 2019.
  99. L Bonfiglio, P Perdikaris, G Vernengo, JS de Medeiros, GE Karniadakis, “Improving SWATH Sea-keeping Performance using Multi-Fidelity Gaussian Process and Bayesian Optimization,” Journal of Ship Research 62 (4), 223-240, 2018.
  100. L Bonfiglio, P Perdikaris, J del A´guila, GE Karniadakis, “A probabilistic framework for multidisciplinary design: Application to the hydrostructural optimization of supercavitating hydrofoils,” International Journal for Numerical Methods in Engineering 116 (4), 246-269, 2018.
  101. D Zhang, L Yang, GE Karniadakis, “Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors,” Journal of Computational Physics 374, 121-134, 2018.
  102. M Raissi, Perdikaris P, Karniadakis GE. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational Physics 378, 686-707, 2019.
  103. M Raissi, Karniadakis GE. “Hidden physics models: Machine learning of nonlinear partial differential equations.” Journal of Computational Physics. 2018 March 15; 357:125-41.
  104. M. Raissi, P. Perdikaris, G.E. Karniadakis, “Inferring solutions of differential equations using noisy multi-fidelity data.” J. Comp. Phys, vol. 335, 736-746, 2017, doi.org/10.1016/j.jcp.2017.01.060.
  105. P. Perdikaris, D. Venturi and G. E. Karniadakis, “Multi-fidelity information fusion algorithms for high-dimensional systems and massive data sets”, SIAM J. Sci. Comput., 38(4), B521-538, 2016.
  106. P. Perdikaris and G. E. Karniadakis. “Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond,” Journal of The Royal Society Interface, 13.118 (2016): 20151107.
  107. P. Perdikaris, D. Venturi, J.O. Royset and G.E. Karniadakis, “Multi-fidelity modeling via recursive co-kriging and Gaussian Markov random fields,” Proc. Roy. Soc. A 471, 20150018, DOI: 10.1098/rspa2015.0018, 2015.
  108. L. Parussini, D. Venturi, P. Perdikaris, G.E. Karniadakis, “Multi-fidelity Gaussian process regression for prediction of random fields.” J. Comput. Phys. 2017, 336, 36-50.
  109. M. Raissi, P. Perdikaris, G. E. Karniadakis, ”Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations”, SIAM J. Sci. Comput. 40(1), A172-A198, 2018.
  110. L. Bonfiglio, P. Perdikaris, S. Brizzolara, G.E. Karniadakis, “Multi-fidelity optimization of super- cavitating hydrofoils”, Comput. Methods Appl. Mech. Engrg. 332, 63-85, 2018.
  111. M. Raissi, P. Perdikaris, G.E. Karniadakis, “Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations,” arXiv:1711.10561v1.
  112. M. Raissi, P. Perdikaris, G.E. Karniadakis, “Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations,” arXiv:1711.10566v1.
  113. Y.H. Tang, D. Zhang, G.E. Karniadakis, “An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Field”, Sept 2017, arXiv:1709.09235v3, J. Chem. Phys. (COVER), 148, no. 3 (2018): 034101.
  114. L. Zhao, Z. Li, B. Caswell, J. Ouyang, G.E. Karniadakis, ”Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows”, Sept 2017, arXiv:1709.06228v1, to appear in J. Comp. Phys., 363: 116-127, 2018.
  115. . M. Xu, D.P. Papageorgiou, S.Z. Abidi, M. Dao, H. Zhao, and G.E. Karniadakis, “A deep convolutional neural network for classification of red blood cells in sickle cell anemia,” PLOS Computational Biology, 13(10): e1005746, 2017.
  116. G. Pang, P. Perdikaris, W. Cai, G.E. Karniadakis, “Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization.” Journal of Computational Physics. 2017 Nov 1;348:694-714.
  117. P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence, and G. E. Karniadakis, “Nonlinear information fusion algorithms for data-efficient multi-fidelity modeling.” P. R. Soc. A. 473(2198), 2017.
  118. M. Raissi, P. Perdikaris, G.E. Karniadakis, “Machine learning of linear differential equations using Gaussian processes.” Journal of Computational Physics, 348, 683-693, 2017.
  119. L. Bonfiglio, P. Perdikaris, S. Brizzolara, G.E. Karniadakis, “A multi-fidelity framework for investigating the performance of super-cavitating hydrofoils under uncertain flow conditions.” In 19th AIAA Non-Deterministic Approaches Conference (p. 1328), 2017.
  120. P. Prempraneerach, P. Perdikaris, G.E. Karniadakis, C. Chryssostomidis, “Sea Surface Temperature estimation from satellite observations and in-situ measurements using multifidelity Gaussian Process regression.” In Digital Arts, Media and Technology (ICDAMT), International Conference on (pp. 28-33). IEEE, 2017
  121. M. Raissi, P. Perdikaris, and G. E. Karniadakis, ”Numerical Gaussian processes for time-dependent and non-linear partial differential equations.” SIAM J. Sci. Comput. 40(1), A172-A198, 2018.
  122. M. Raissi, G.E. Karniadakis, “Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations.” arXiv preprint arXiv:1708.00588, 2017.
  123. H. Babaee, P. Perdikaris, C. Chryssostomidis, G.E. Karniadakis, “Multi-fidelity modelling of mixed convection based on experimental correlations and numerical simulations.” Journal of Fluid Mechan- ics. 2016 Dec;809:895-917.
  124. S. Lee, I.G., Kevrekidis, G.E. Karniadakis, “A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion.” Journal of Computational Physics, 344, 516-533, 2017.
  125. S. Lee, I.G., Kevrekidis, G.E. Karniadakis “A general CFD framework for fault-resilient simulations based on multi-resolution information fusion”. Journal of Computational Physics, 347, 290-304, 2017
  126. S. Lee, I.G., Kevrekidis, G.E. Karniadakis, “Resilient algorithms for reconstructing and simulating gappy flow fields in CFD”. Fluid Dynamics Research, 47(5), 051402, 2015.
  127. A. Yakhot, T. Anor, G.E. Karniadakis, ”A reconstruction method for gappy and noisy arterial flow data”, IEEE transactions on medical imaging. 2007 Dec;26(12):1681-97.
  128. H. Gunes, S. Sirisup, G.E. Karniadakis, ”Gappy data: To Krig or not to Krig?”, Journal of Com-putational Physics. 2006 Feb 10;212(1):358-82.

Fractional and Stochastic PDEs/Uncertainty Quantification

  1. M Carlson, X Zheng, H Sundar, GE Karniadakis, RM Kirby, “An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains,” Computer Physics Communications 261, 107695, 2021.
  2. X Li, Z Mao, N Wang, F Song, H Wang, GE Karniadakis, “A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation,” Computer Methods in Applied Mechanics and Engineering 366, 113053, 2020.
  3. A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M. M. Meerschaert, M. Ainsworth, G. E. Karniadakis, “What is the fractional”, J. Comput. Phys., Vol. 404, pp. 109009, 2020.
  4. H Zhang, X Jiang, F Zeng, GE Karniadakis, “A stabilized semi-implicit Fourier spectral method for nonlinear space- fractional reaction-diffusion equations,” Journal of Computational Physics 405, 10914, 2020.
  5. L Guo, F Zeng, I Turner, K Burrage, GE Karniadakis, “Efficient multistep methods for tempered fractional calculus: algorithms and simulations,” SIAM Journal on Scientific Computing 41 (4), A2510-A2535, 2019.
  6. N Wang, Z Mao, C Huang, GE Karniadakis, “A spectral penalty method for two-sided fractional differential equations with general boundary conditions,” SIAM Journal on Scientific Computing 41 (3), A1840-A1866, 2019.
  7. T Zhao, Z Mao, GE Karniadakis, “Multi-domain spectral collocation method for variable-order non-linear fractional differential equations,” Computer Methods in Applied Mechanics and Engineering 348, 377-395, 2019.
  8. T Wang, F Song, H Wang, GE Karniadakis, “Fractional Gray–Scott model: Well-posedness, discretization, and simulations,” Computer Methods in Applied Mechanics and Engineering 347, 1030- 1049, 2019.
  9. F Song, GE Karniadakis, “Fractional magneto-hydrodynamics: Algorithms and applications,” Journal of Computational Physics 378, 44-62, 2019.
  10. Z Zhang, W Deng, GE Karniadakis, “A Riesz basis Galerkin method for the tempered fractional Laplacian,” SIAM Journal on Numerical Analysis 56 (5), 3010-3039, 2018.
  11. F Zeng, I Turner, K Burrage, GE Karniadakis, “A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations,” SIAM Journal on Scientific Computing 40 (5), A2986-A3011, 2018.
  12. Z. Zhang, W. Deng, G.E. Karniadakis, “A Riesz basis Galerkin method for the tempered fractional Laplacian”, https://arxiv.org/pdf/1709.10415.pdf, SIAM Journal on Numerical Analysis, to appear, 2018.
  13. A. Lischke, M. Zayernouri, G. E. Karniadakis, “A Petrov-Galerkin spectral method of linear complexity for fractional multi-term ODEs on the half line”, SIAM J. Sci. Comput., Vol. 39 (2017), No. 3, pp. A922-A946.
  14. Z. Mao, G.E. Karniadakis, “A Spectral method (of exponential convergence) for singular solutions of the diffusion equation with general two-sided fractional derivative”, SIAM Journal on Numerical Analysis, 56(1), 24-49, 2018.
  15. F. Song, G.E. Karniadakis, “Fractional spectral vanishing viscosity method: Application to the quasi-geostrophic equation”, Chaos, Solitons Fractals, 102, pp.327-332, 2017.
  16. F. Zeng, Z. Mao, G.E. Karniadakis, “A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities.” SIAM J. Sci. Comput. 2017, 39(1);A360-A383.
  17. F. Song, F. Zeng, W. Cai, W. Chen, G. E. Karniadakis, “Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes.” Computers and Mathematics with Applications, 2017, 73; 1286- 1297.
  18. Z. Mao, G.E. Karniadakis, “Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods.” J. Comput. Physics, 2017, 336; 143-163.
  19. X. Chen, F. Zeng, G.E. Karniadakis, “A tunable finite difference method for fractional differential equations with non- smooth solutions.” Comput. Methods Appl. Mech. Engrg. 2017, 318; 193-214.
  20. C. Kim, O. Borodin and G.E. Karniadakis, “Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids”, J. Comp. Phys., 302, 485-508, 2016.
  21. W. Cao, Z. Zhang and G.E. Karniadakis, “Implicit-explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions”, SIAM J. Sci Comput., 38(5), A3070-A3093, 2016.
  22. J. Suzuki, M. Zayernouri and G.E. Karniadakis, “Fractional-order uniaxial visco-elasto-plastic models for structural analysis”, Computer Methods in Applied Mechanics and Engineering (2016), pp. 443-467, DOI information: 10.1016/j.cma.2016.05.030, 2016.
  23. Y. Yu, P. Perdikaris and G.E. Karniadakis, “Fractional Modeling of Viscoelasticity in 3D Cerebral Arteries and Aneurysms,” J. Comput. Phys., 323, pp.219-242, 2016.
  24. F. Song, C. Xu and G.E. Karniadakis, “A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations,” Computer Methods in Applied Mechanics and Engineering, 305, 376-404, 2016.
  25. F. Zeng, Z. Zhang and G.E. Karniadakis, “Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations,” J. Comput. Phys. 307, 15-33, 2016.
  26. F. Zeng, Z. Zhang and G.E. Karniadakis, “Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions”, Computer Methods in Applied Mechanics and Engineering. 2017 Dec 1;327:478-502.
  27. M. Zayernouri, M. Ainsworth and G.E. Karniadakis, “Tempered Fractional Sturm-Liouville eigen-problems,” SIAM J. Sci. Comput.. 37(4) A1777-A1800, DOI: 10.1137/140985536, 2015.
  28. H. Cho, Y. Yang, D. Venturi and G.E. Karniadakis, “Algorithms for propagating uncertainty across heterogeneous domains,” SIAM J. Sci. Comput. 37(6), A3030-A3054, DOI: 10.1137/140992060, 2015.
  29. Z. Zhang, B. Rozovskii, and G.E. Karniadakis, “Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise”, Numerische Mathematik, pp.1-29, (2015).
  30. X. Zhao, Z.Z. Sun, and G.E. Karniadakis, “Second-order approximations for variable order fractional derivatives: Algorithms and applications”, Journal of Computational Physics, 293, 184-200, (2015).
  31. H. Cho, D. Venturi and G.E. Karniadakis, “Numerical methods for high-dimensional probability density function equations,” J. Comput. Phys. 305, 817-837, 2016, DOI:10.1016/j.jcp.2015.10.030.
  32. F. Zeng, Z. Zhang and G.E. Karniadakis, “A generalized spectral collocation method with turnable accuracy for variable-order fractional differential equations,” SIAM J. Sci Comput. 37(6), A2710- A2732, DOI: 10.1137/141001299, 2015.
  33. Z. Zhang, F. Zeng and G.E. Karniadakis “Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations,” SIAM J. Numer. Anal., 53(4) 2074-2096, 2015.
  34. M. Zayernouri and G.E. Karniadakis, “Fractional spectral collocation methods for linear and non-linear variable order FPDEs,” J. Comput. Phys. 293, 312-338, DOI: 10.1016/j.jcp.1014.12.001, 2015.
  35. W. Cao, Z. Zhang and G.E. Karniadakis “Time-splitting schemes for fractional differential equations I: Smooth solutions,” SIAM J. Sci. Comput. 37(4), A1752-A1776, DOI: 10.1137/140996495, 2015.
  36. Zheng M.* and G.E. Karniadakis. “Numerical methods for SPDEs with tempered stable processes”, SIAM J. Sci. Comp., 37(3): A1197-A1217, DOI: 10.1137/140966083, 2015.
  37. Zheng, M., Rozovsky, B., Karniadakis, G. E. “Adaptive Wick–Malliavin Approximation to Non-linear SPDEs with Discrete Random Variables.” SIAM Journal on Scientific Computing”, 37(4), A1872-A1890, 2015.
  38. W. Cao, Z. Zhang and G.E. Karniadakis, “Numerical methods for stochastic delay differential equations via the Wong-Zakai approximation,” SIAM J. Sci. Comput, 37(1), A295-A318, 2015.
  39. B. Yildirim and G.E. Karniadakis, “Stochastic simulations of ocean waves: An uncertainty quantification study,” Ocean Modeling, 86, 15-35, 2015.
  40. M. Zayernouri, M. Ainsworth and G.E. Karniadakis, “A unified Petrov-Galerkin spectral method for fractional PDEs,” Computer Methods in Applied Mechanics and Engineering, 283, 1545-1569, DOI/10.1016/j.cma.2014.10.051, 2015.
  41. Zheng M., X. Wan, and GE Karniadakis. “Adaptive-multi-element polynomial chaos with discrete measure: Algorithms and application to SPDEs”, Applied Numerical Mathematics, 90, 91-110, 2015.
  42. H. Cho, D. Venturi and G.E. Karniadakis, “Statistical analysis and simulation of random shocks in Burgers turbulence,” Proceedings of the Royal Society A, 470, 20140080, DOI: 10.1098/rspa.s014.0080, 2014.
  43. Zhang, Z., X. Yang*, G. Marucci, P. Maffezzoni, I. Abe M. Elfadel, G.E. Karniadakis, and L. Daniel. “Stochastic testing simulator for integrated circuits and MEMS: Hierarchical and sparse techniques.” In Custom Integrated Circuits Conference (CICC), 2014 IEEE Proceedings of the, pp. 1-8. IEEE, 2014.
  44. Choi M.*, T. Sapsis, and G.E. Karniadakis, “On the equivalence of dynamically orthogonal and dynamically bi-orthogonal methods: Theory and numerical simulations”, Journal of Computational Physics, 270, 1-20, 2014.
  45. M. Zayernouri, W. Cao, Z. Zhang, G. E. Karniadakis, “Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations”, SIAM J. Sci. Comput.,” 36 (6), B904B929, 2014.
  46. Z. Zhang*, M.V. Tretyakov, B. Rozovskii and G.E. Karniadakis, “A recursive sparse grid collocation method for differential equations with white noise”, SIAM J. Sci. Comput. 36(4), A1652-A1677, 2014.
  47. M. Zayernouri* and G.E. Karniadakis, “Discontinuous spectral element methods for time-and space-fractional advection equations”, SIAM J. Sci. Comput. 36(4), B684-B707, 2014.
  48. D. Venturi and G.E. Karniadakis, “Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems”, Proc. R. Soc. A, 470, 20130754, 2014.
  49. D. Venturi, X. Wan, R. Mikulevicius, B. Rozovskii and G.E. Karniadakis, “Wick-Malliavin approximation to nonlinear stochastic PDEs: Analysis and Simulation”, Proc. R. Soc. A, 34:157-167, 2014.
  50. M. Zayernouri* and G.E. Karniadakis, “Fractional spectral collocation methods”, SIAM J. Sci. Comput. 36(1):A40- A62, 2014.
  51. M. Zayernouri* and G.E. Karniadakis, “Exponentially accurate spectral and spectral element methods for fractional ODEs”, J. Comput. Phys., 247:460-480, 214.
  52. M. Choi*, T. Sapsis and G.E. Karniadakis, “A convergence study for SPDEs using combined polynomial chaos and dynamically-orthogonal schemes,” J. Comp. Phys. 245, 281-301, 2013.
  53. M. Zayernouri* and G.E. Karniadakis, “Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation,” J. Comp. Phys., 252, 495-517, 2013.
  54. H. Cho, D. Venturi and G.E. Karniadakis, “Karhunen-Loeve expansion for multi-correlated processes,” Probabilistic Engineering Mechanics, 34:157-167, 2013.
  55. H. Cho, D. Venturi and G.E. Karniadakis, “Adaptive discontinuous Galerkin method for response-excitation PDF equations,” SIAM J. Sci. Comput., vol. 35(4), pp. B890-B911, 2013.
  56. M. Zayernouri, S-W. Park, D.M. Tartakovsky and G.E. Karniadakis, “Stochastic smoothed profile method for modeling random roughness in flow problems,” Comput. Methods Appl. Mech. Engrg., vol. 263, pp. 99-112, 2013.
  57. D. Venturi, D.M. Tartakovsky, A.M. Tartakovsky and G.E. Karniadakis, “Exact PDF equations and closure approximations for advective-reactive transport,” J. Comp. Phys., vol. 243, pp. 323-343, 2013.
  58. X. Yang and G.E. Karniadakis, “Reweighted l1 minimization method for stochastic elliptic differential equations,” J. Comp. Phys., vol.i 248, pp. 87-108, 2013.
  59. Z. Zhang, X. Yang, G. Lin and G.E. Karniadakis, “Numerical solution of the Stratonovich-and Ito-Euler equations: Application to the stochastic piston problem,” J. Comp. Phys., vol. 236, pp. 15-27, 2013.
  60. Z. Zhang*, B. Rosvoskii, M.V. Tretyakov and G.E. Karniadakis, “A multi-stage Wiener chaos expansion method for stochastic advection-diffusion reaction equations,” SIAM J. Sci. Comput., 34(2), A914-A936, 2012.
  61. D. Venturi and G.E. Karniadakis, “New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs,” J. Comp. Phys., vol. 231, pp. 7450-7474, 2012.
  62. D. Venturi, T. Sapsis, H. Cho and G.E. Karniadakis, “A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems,” Proc. Roy. Soc. A, vol. 468, pp. 759-783, 2012.
  63. Z. Zhang, M. Choi, and G.E. Karniadakis, “Error estimates for the ANOVA method with polynomial chaos interpolation:Tensor product functions,” SIAM J. Sci. Comp., vol. 34(2), pp. A1165-A1186, 2012.
  64. D. Venturi, M. Choi* and G.E. Karniadakis, “Supercritical quasi-continuum states in stochastic Rayleigh-Bernard convection,” Int. J. Heat Mass Transfer, vol. 55, pp. 3732-3743, 2012.
  65. X. Yang, M. Choi, and G. Lin and G.E. Karniadakis, “Adaptive ANOVA decomposition of stochastic incompressible and compressible flows,” J. Comp. Phys., vol. 231, pp. 1587-1614, 2012.
  66. D. Venturi and G. E. Karniadakis, “Differential constraints for the probability density function of stochastic solutions to the wave equation,” International Journal for Uncertainty Quantification, vol. 2(3), pp. 195-213, 2012.
  67. M. Gerritsma, J-B. van der Steen, P. Vos and G.E. Karniadakis, “Time-dependent generalized polynomial chaos,” J. Comput. Phys., 229:8333-8363, 2010.
  68. P. Prempraneerach, F. Hover, M. Triantafyllou, and G.E. Karniadakis, “Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods,” Reliability Engineering and System Safety, vol. 95, pp. 632-646, 2010.
  69. J. Foo* and G.E. Karniadakis, “Multi-element probabilistic collocation method in high dimensions,” J. Comp. Phys., vol. 229(5), pp. 1536-1557, 2010.
  70. D. Venturi, X. Wan and G.E. Karniadakis, “Stochastic bifurcation analysis of Rayleigh-Benard convection,” J. Fluid Mech., vol. 650, pp. 391-413, 2010.
  71. G. Lin* and G.E. Karniadakis, “Sensitivity analysis and stochastic simulations of non-equilibrium plasma flow,” Int. J. Num. Meth. Engng., vol. 80, pp. 738-766, 2009.
  72. X. Wan*, B. Rozovskii and G.E. Karniadakis, “A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus,” Proc. Nat. Acad. Sciences, vol. 106, no. 34, pp. 14189-14194, 2009.
  73. G. Lin*, C.-H. Su and G.E. Karniadakis, “Stochastic modeling of random roughness in shock scattering problems: Theory and simulations,” Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 3420-3434, 2008.
  74. X. Wan* and G.E. Karniadakis, “Error control in multi-element generalized polynomial chaos method for elliptic problems with random coefficients,” Communication in Computational Physics, vol. 5, pp. 793-820, 2009.
  75. X. Wan* and G.E. Karniadakis, “Solving elliptic problems with non-Gaussian spatially dependent random coefficients: algorithms, error analysis and applications,” Comput. Methods Appl. Mech. Engr., vol. 198, pp. 1985- 1995, 2009.
  76. J. Foo, X. Wan, and G.E. Karniadakis, “The multi-element probabilistic collocation method: error analysis and simulation,” J. Comp. Phys., vol. 227, pp. 9572-9595, 2008.
  77. D. Venturi, X. Wan and G.E. Karniadakis, “Stochastic low dimensional modeling of random laminar wake past a circular cylinder,” Journal of Fluid Mechanics, vol. 606, pp. 339-367, 2008.
  78. G. Lin, X. Wan, C.-H. Su and G.E. Karniadakis, “Stochastic fluid mechanics,” IEEE Computing in Science and Engineering (CiSE), vol. 9, pp. 21-29, 2007.
  79. G. Lin*, C.-H. Su and G.E. Karniadakis, “Random roughness enhances lift in supersonic flow,” Phys. Rev. Let., vol 99, (10), 104501, 2007.
  80. J. Foo*, Z. Yosibash and G.E. Karniadakis, “Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties,” Comput. Methods Appl. Mech. Engr., vol. 196, pp. 4250- 4271, 2007.
  81. G. Lin*, C.-H. Su and G.E. Karniadakis, “Predicting shock dynamics in the presence of uncertainties,” J. Comp. Phys., vol. 217, pp. 260-276, 2006.
  82. X. Wan* and G.E. Karniadakis, “Stochastic heat transfer enhancement in a grooved channel,” J. Fluid Mech., vol. 565, pp. 255-278, 2006.
  83. X. Wan* and G.E. Karniadakis, “Beyond Wiener-Askey expansions: Handling arbitrary PDFs,” Journal of Scientific Computing, vol. 27, pp. 455-464, 2006.
  84. X. Wan* and G.E. Karniadakis, “Multi-element generalized polynomial chaos for arbitrary probability measures,” SIAM Journal of Scientific Computing, vol. 28(3), pp. 901-928, 2006.
  85. X. Wan* and G.E. Karniadakis, “Long-term behavior of polynomial chaos in stochastic flow simulations,” Comput. Methods Appl. Mech. Engrg., vol. 195, pp. 5528-5596, 2006.
  86. H. Gunes, S. Sirisup* and G.E. Karniadakis, “Gappy data: To Krig or not to Krig?,” Journal of Computational Physics, vol. 212(1), pp. 358-382, 2006.
  87. G. Lin*, L. Grinberg and G.E. Karniadakis, “Numerical studies of the stochastic Korteweg de Vries equation,” Journal of Computational Physics, vol. 213(2), pp. 676-703, 2006.
  88. X. Wan* and G.E. Karniadakis, “An adaptive multi-element generalized polynomial chaos method for stochastic differential equations,” J. Comp. Phys., vol. 209(2), pp. 617-642, 2005.
  89. X. Wan, D. Xiu, and G.E. Karniadakis, “Stochastic solutions for the two-dimensional advection-diffusion equation,” SIAM J. Sci. Comput., vol. 26(2), pp. 578-590, 2004.
  90. D. Lucor* and G.E. Karniadakis, “Adaptive generalized polynomial chaos for nonlinear random oscillators,” SIAM J. Sci. Comput., vol. 26(2), pp. 720-735, 2004.
  91. D. Xiu* and G.E. Karniadakis, “Supersensitivity due to uncertain boundary conditions,” Int. J. Num. Meth. Eng.’, vol. 61, pp. 2114-2138, 2004.
  92. G. Lin*, C.-H. Su and G.E. Karniadakis, “The stochastic piston problem,” Proc. National Academy of Sciences, vol. 101, pp. 15840-15845, 2004.
  93. D. Lucor* and G.E. Karniadakis, “Noisy inflows cause a shedding-mode switching in flow past an oscillating cylinder,” Phys. Rev. Lett., vol. 92(15), 154501, 2004. (featured on the cover).
  94. D. Venturi and G.E. Karniadakis, “Gappy data and reconstruction procedures for flow past cylinder,” J. Fluid Mech., vol. 519, pp. 315-336, 2004.
  95. D. Lucor*, C.-H. Su and G.E. Karniadakis, “Generalized polynomial chaos and random oscillators,” Int. J. Num. Meth. Eng., vol. 60(3), pp. 571-596, 2004.
  96. D. Lucor* and G.E. Karniadakis, “Predictability and uncertainty in flow-structure interactions,” European Journal of Mechanics B/Fluids, vol. 23, pp. 41-49, 2004.
  97. D. Lucor, D. Xiu, C.-H. Su and G.E. Karniadakis, “Predictability and uncertainty in CFD,” Int. J. Num. Meth. Fluids, vol. 43(5), pp. 485-505, 2003.
  98. D. Xiu* and G.E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comp. Phys., vol. 187, pp. 137-167, 2003.
  99. D. Xiu* and G.E. Karniadakis, “A new stochastic approach to transient heat conduction modeling with uncertainty,” Int. J. Heat Mass Transfer, vol. 46, pp. 4681-4693, 2003.
  100. D. Xiu* and G.E. Karniadakis, “Modeling uncertainty in flow simulations via Generalized Polynomial Chaos,” J. Comp. Phys., vol. 187, pp. 137-167, 2003.
  101. D. Xiu* and G.E. Karniadakis, “The Wiener-Askey Polynomial Chaos for stochastic differential equations,” SIAM Journal of Scientific Computing, vol 24, no. 2, pp. 619-644, 2002.
  102. D. Xiu, D. Lucor, C.-H. Su and G.E. Karniadakis, “Stochastic modeling of flow-structure interactions using Generalized Polynomial Chaos,” J. Fluids Engineering, vol. 124, pp. 51-59, 2002.
  103. M. Jardak*, C.-H. Su and G.E. Karniadakis, “Spectral Polynomial Chaos solutions of the stochastic advection equation,” J. Sci. Comp., vol. 17, pp. 319-338, 2002.
  104. D. Xiu* and G.E. Karniadakis, “Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos,” Comput. Methods Appl. Mech. Engrg., vol. 191, pp. 4927-4948, 2002.

Spectral Element and Discontinuous Galerkin Methods

  1. Z Wang, X Zheng, C Chryssostomidis, GE Karniadakis, “A phase-field method for boiling heat transfer,” Journal of Computational Physics, 110239, 2021.
  2. Z Wang, S Dong, MS Triantafyllou, Y Constantinides, GE Karniadakis, “A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio,” Journal of Computational Physics 397, 108832, 2019.
  3. Z Wang, MS Triantafyllou, Y Constantinides, GE Karniadakis, “A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems,” Computers Fluids 172, 84-96, 2019.
  4. X. Zhen and G.E. Karniadakis, “A Phase-field/ALE method for simulating fluid-structure interactions in two-phase flow,” Computer Methods in Applied Mechanics and Engineering, 309, 19-40, 2016.
  5. X. Zheng, H. Babaee, S. Dong, C. Chryssotomidis, and G.E. Karniadakis, “A phase-field method for 3D simulation of two-phase heat transfer,” Int. J. of Heat and Mass Transfer, 82, 282-298, DOI: 10.1016/j.jijheatmasstransfer.2014.11.052, 2015.
  6. S. Dong, G.E. Karniadakis and C. Chryssostomidis, “A robust and accurate outflow boundary condition for incompressible flow simulations on severely truncated unbounded domains,” J. Comput. Phys., 261:83-105, 2014.
  7. Y. Yue, H. Baek, and G.E. Karniadakis, “Generalized fictitious methods for fluid-structure interactions: Analysis and simulations,” J. Comp. Phys., vol. 245, 317-346, 2013.
  8. H. Baek* and G.E. Karniadakis, “A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping,” J. Comp. Phys., vol. 231(2), 629-652, 2012.
  9. B. Yildirim* and G.E. Karniadakis, “A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation,” J. Comp. Phys., vol. 231, pp. 4921-4953, 2012.
  10. Y. Yue, H. Baek, M.L. Bittencourt and G.E. Karniadakis, “Mixed spectral/hp element formulation for nonlinear elasticity,” Computer Methods in Applied Mechanics and Engineering, vol. 213-216, pp. 42-57, 2012.
  11. H. Baek* and G.E. Karniadakis, “Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations,” J. Comp. Phys., vol. 230, pp. 4384-4402, 2011.
  12. X. Luo*, A. Beskok and G.E. Karniadakis, “Modeling electrokinetic flows by the smoothed profile method,” J. Comp. Phys., vol. 229, pp. 3828-3847, 2010.
  13. X. Luo*, M. Maxey and G.E. Karniadakis, “Smoothed Profile Method for Particulate Flows: Error Analysis and Simulations,” J. Comp. Phys., vol. 228, pp. 1750-1769, 2009.
  14. L. Grinberg* and G.E. Karniadakis, “Hierarchical spectral basis and Galerkin formulation using barycentric quadrature grids in triangular elements,” Journal of Engineering Mathematics, 56(3), 289-306, 2007.
  15. R.M. Kirby*, Z. Yosibash and G.E. Karniadakis, “Towards stable coupling methods for high-order discretization of fluid-structure interaction: Algorithms and observations,” J. Comp. Phys., vol. 223, pp. 489-518, 2007.
  16. X. Wan* and G.E. Karniadakis, “A sharp error estimate for the fast Gauss transform,” J. Comp. Phys., vol. 219, pp. 7-12, 2006.
  17. G. Lin* and G.E. Karniadakis, “A discontinuous Galerkin method for two-temperature plasmas,” Comput. Methods Appl. Mech. Engrg., vol. 195, pp. 3504-3527, 2006.
  18. R.M. Kirby* and G.E. Karniadakis, “Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems,” Journal of Scientific Computing, vols. 22-23 (1-3), pp. 385-411, 2005.
  19. D. Xiu*, S.J. Sherwin, S. Dong and G.E. Karniadakis, “Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows,” Journal of Scientific Computing, vol. 25, pp 323-346, 2005.
  20. S. Dong, D. Liu*, M.R. Maxey and G.E. Karniadakis, “Spectral distributed Lagrange multiplier method: Algorithm and benchmark tests,” Journal of Computational Physics, vol. 195, pp. 695-717, 2004.
  21. R.M. Kirby* and G.E. Karniadakis, “De-aliasing on non-uniform grids: algorithms and applications,” J. Comp. Phys., vol. 191, pp. 249-264, 2003.
  22. D. Liu*, M. Maxey and G.E. Karniadakis, “A fast method for particulate microflows,” J. Micro- electromechanical Systems, vol. 11(6), pp. 691-702, 2002.
  23. R.M. Kirby* and G.E. Karniadakis, “Coarse resolution turbulence simulations using SVV-LES,” J. Fluids Eng., vol. 177, p. 133, 2002.
  24. J.Xu, D. Xiu and G.E. Karniadakis, “A Semi-Lagrangian method for turbulence simulations using mixed spectral discretizations,” J. Sci. Comp., vol. 17, pp. 585-597, 2002.
  25. C. Evangelinos, D. Lucor, C.-H. Su and G.E. Karniadakis, “Flow-induced vibrations of non-linear cables, Part I: Models and Algorithms,” Int. J. Num. Meth. Engin., vol. 55, pp. 535-556, 2002.
  26. R.M. Kirby*, G.E. Karniadakis, O. Mikulchenko and K. Mayaram, “An integrated simulator for coupled domain problems in MEMS,” J. Microelectromechanical Systems, vol. 10(3), pp. 379-399, 2001.
  27. D. Xiu* and G.E. Karniadakis, “A semi-Lagrangian high-order method for Navier-Stokes equations,” J. Comp. Phys., vol. 172, pp. 658-684, 2001.
  28. G.S. Karamanos and G.E. Karniadakis, “A spectral vanishing viscosity method for large-eddy simulations,” J. Comp. Phys., vol. 162, pp. 22-50, 2000.
  29. J. Trujillo* and G.E. Karniadakis, “A penalty method for the vorticity-velocity formulation,” J. Comp. Phys., vol. 149, pp. 32-58, 1999.
  30. R.M. Kirby, T.C. Warburton, I. Lomtev* and G.E. Karniadakis, “A discontinuous Galerkin spectral/hp method on hybrid grids,” J. Appl. Num. Math., vol. 33, pp. 393-405, 1999.
  31. I. Lomtev, R.M. Kirby, and G.E. Karniadakis, “A discontinuous Galerkin ALE method for compressible viscous flows in moving domains,” J. Comp. Phys., vol. 155, pp. 128-159, 1999.
  32. T.C. Warburton* and G.E. Karniadakis, “A discontinuous Galerkin method for the viscous MHD equations,” J. Comp. Phys., vol. 152, pp. 608-641, 1999.
  33. T.C. Warburton, I. Lomtev, Y. Du, S.J. Sherwin, and G.E. Karniadakis, “Galerkin and discontinuous Galerkin spectral/hp methods,” Comp. Meth. Appl. Mech. Engr., vol. 175, pp. 343-359, 1999.
  34. T.C. Warburton, S.J. Sherwin, and G.E. Karniadakis, “Basis functions for triangular and quadrilateral high-order elements,” SIAM J. Scientific Computing, vol. 20(5), pp. 1671-1695, 1999.
  35. I. Lomtev*, and G.E. Karniadakis, “A discontinuous Galerkin method for the Navier-Stokes equations,” Int. J. Num. Meth. Fluids, vol. 29, pp. 587-603, 1999.
  36. I. Lomtev*, C.B. Quillen and G.E. Karniadakis, “Spectral/hp methods for viscous compressible flows on unstructured 2D meshes,” J. Comp. Phys., vol. 144, pp. 325-357, 1998.
  37. S.J. Sherwin, T.C. Warburton, and G.E. Karniadakis, “Spectral/hp methods for elliptic problems on hybrid grids,” Contemporary Mathematics, vol. 218, p. 191-215, 1998.
  38. S.J. Sherwin* and G.E. Karniadakis, “Tetrahedral hp finite elements: Algorithms and flow simulations,” J. Comp. Phys., vol. 124, p. 14, 1996.
  39. D. Pathria G.E. Karniadakis, “Spectral element methods for elliptic problems in non-smooth domains,” J. Comp. Phys., vol. 122, p. 83, 1995.
  40. S.J. Sherwin* and G.E. Karniadakis, “A triangular spectral element method; Applications to the incompressible Navier-Stokes equations,” C.M.A.M.E., vol. 123, p. 189, 1995.
  41. S.J. Sherwin* and G.E. Karniadakis, “A new triangular and tetrahedral basis for high-order finite element methods,” Int. J. Num. Meth. Eng., vol. 38, p. 3775, 1995.
  42. R.D. Henderson* and G.E. Karniadakis, “Unstructured spectral element methods for simulation of turbulent flows,” J. Comp. Phys., vol. 122 p. 191, 1995.
  43. J. Giannakouros* and G.E. Karniadakis, “A spectral element-FCT method for the compressible Euler equations,” J. Comp. Phys., vol 115, p. 65, 1994.
  44. J. Giannakouros*, D. Sidilkover G.E. Karniadakis, “Spectral element-FCT method for the one-and two-dimensional Euler equations,” C.M.A.M.E., vol. 116, p. 113, 1994; also in ICOSAHOM, p. 113, (eds. C. Bernardi Y. Maday), North Holland, 1992.
  45. D. Sidilkover G.E. Karniadakis, “Non-oscillatory spectral element Chebyshev method for shock wave calculations,” Proc. 5th Conf. on Domain Decomposition Methods, SIAM, 1991, also in J. Comp. Phys., vol. 107, p. 10, 1993.
  46. G.E. Karniadakis, M. Israeli S.A. Orszag, “High-order splitting methods for the incompressible Navier-Stokes equations,” J. Comp. Phys., vol. 97, p.414, 1991.
  47. R.D. Henderson* G.E. Karniadakis, “Hybrid spectral element-low order methods for incompressible flows,” J. Sci. Comp., vol. 6, No. 2, p. 79, 1991.
  48. J. Giannakouros* G.E. Karniadakis, “Spectral element-FCT method for scalar hyperbolic laws,” Proc. 3rd Int. Conf. on Hyperb. Problems, vol. 1, p. 446, 1990 (also in Int. J. Num. Meth. Fluids, 14, p.707, 1992).
  49. G.E. Karniadakis, “Spectral element-Fourier methods for incompressible turbulent flows,” C.M.A.M.E., vol. 80, p. 362, 1990. (also in Proc. ICOSAHOM’89 Conf., Como, 1989).
  50. A.G. Tomboulides*, M. Israeli, G.E. Karniadakis, “Efficient removal of boundary-divergence errors in time-splitting methods,” J. Sci. Comp., vol. 4, p. 291, 1989.
  51. G.E. Karniadakis, “Spectral element simulations of laminar and turbulent flows in complex geometries,” Appl. Num. Math., vol. 6, p. 85, 1989.
  52. N.K. Ghaddar, G.E. Karniadakis A.T. Patera, “A conservative isoparametric spectral element method for forced convection: Application to fully developed flow in periodic geometries,” Num. Heat Transfer, vol., 9, p.277, 1986.

Biomedical/Multiscale/Microfluidic Modeling

  1. S Wang, S Ma, H Li, M Dao, X Li, GE Karniadakis, “Two-component macrophage model for active phagocytosis with pseudopod formation,” Biophysical Journal, 2024.
  2. G Li, H Li, PA Ndou, M Franco, Y Qiang, X Li, PA Buffet, M Dao, “Red blood cell passage through deformable interendothelial slits in the spleen: Insights into splenic filtration and hemodynamics,” …bioRxiv, 2024.02. 22.
  3. H Li, ZL Liu, L Lu, P Buffet, GE Karniadakis. “How the spleen reshapes and retains young and old red blood cells: A computational investigation,” PLoS computational biology. 2021 Nov 1;17(11):e1009516.
  4. ZL Liu, H Li, Y Qiang, P Buffet, M Dao, GE Karniadakis, “Computational modeling of biomechanics and biorheology of heated red blood cells,” Biophysical Journal. 2021 Nov 2;120(21):4663-71.
  5. A Yazdani, Y Deng, H Li, E Javadi, Z Li, S Jamali, C Lin, JD Humphrey, GE Karniadakis, “Integrating blood cell mechanics, platelet adhesive dynamics and coagulation cascade for modelling thrombus formation in normal and diabetic blood,” Journal of the Royal Society Interface 18 (175), 20200834, 2021.
  6. Y Deng, DP Papageorgiou, X Li, N Perakakis, CS Mantzoros, M. Dao and G.E. Karniadakis, “Quantifying Fibrinogen-dependent Aggregation of Red Blood Cells in Type 2 Diabetes Mellitus,” Biophysical Journal, vol. 119(5), ppp. 900902, 2020.
  7. Y Wang, Z Li, J Ouyang, GE Karniadakis, “Controlled release of entrapped nanoparticles from thermoresponsive hydrogels with tunable network characteristics,” Royal Society of Chemistry, DOI: 10.1039/D0SM00207K, April 2020.
  8. K Sampani, H Li, X Zheng, D Papageorgiou, MO Bernabeu, W Fickweiler, LP Aiello; G Karniadakis, JK Sun, “Computational fluid dynamics (CFD) estimation of thrombus formation in diabetic retinal microaneurysms (MAs),” Investigative Ophthalmology Visual Science June 2020, Vol.61, 5023, Issue 7, June 2020.
  9. X Zheng, A Yazdani, H Li, JD Humphrey, GE Karniadakis, “A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels,” PLoS computational biology 16 (4), e1007709, 2020.
  10. KS Kim, C Kim, GE Karniadakis, EK Lee, JJ Kozak, “Density-dependent finite system-size effects in equilibrium molecular dynamics estimation of shear viscosity: Hydrodynamic and configurational study,” The Journal of Chemical Physics, 151(10):104101, 2019.
  11. L Lu, Z Li, H Li, X Li, PG Vekilov, GE Karniadakis, “Quantitative prediction of erythrocyte sickling for the development of advanced sickle cell therapies,” Science Advances 5 (8), eaax3905, 2019.
  12. M Yin, A Yazdani, GE Karniadakis, “One-dimensional modeling of fractional flow reserve in coronary artery disease: Uncertainty quantification and Bayesian optimization,” Computer Methods in Applied Mechanics and Engineering 353, 66-85, 2019.
  13. KS Kim, MH Han, C Kim, Z Li, GE Karniadakis, EK Lee, “Nature of intrinsic uncertainties in equilibrium molecular dynamics estimation of shear viscosity for simple and complex fluids,” The Journal of Chemical Physics 149 (4), 044510. 2019.
  14. K Zhang, Z Li, M Maxey, S Chen, GE Karniadakis, “Self-cleaning of hydrophobic rough surfaces by coalescence-induced wetting transition,” Langmuir 35 (6), 2431-2442, 2019.
  15. Y Deng, DP Papageorgiou, HY Chang, SZ Abidi, X Li, M Dao, GE Karniadakis, “Quantifying shear-induced deformation and detachment of individual adherent sickle red blood cells,” Biophysical journal 116 (2), 360-371, 2019.
  16. Y Wang, Z Li, J Xu, C Yang, GE Karniadakis, “Concurrent coupling of atomistic simulation and mesoscopic hydrodynamics for flows over soft multi-functional surfaces,” Soft matter 15 (8), 1747- 1757, 2019.
  17. HY Chang, A Yazdani, X Li, KAA Douglas, CS Mantzoros, GE Karniadakis, “Quantifying platelet margination in diabetic blood flow,” Biophysical journal 115 (7), 1371-1382, 2018.
  18. Y Yu, FF Bargos, H You, ML Parks, ML Bittencourt, GE Karniadakis, “A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations,” Computer Methods in Applied Mechanics and Engineering 340, 905-931, 2018.
  19. L Lu, Y Deng, X Li, H Li, GE Karniadakis, “Understanding the Twisted Structure of Amyloid Fibrils via Molecular Simulations,” The Journal of Physical Chemistry B 122 (49), 11302-11310, 2018.
  20. DP Papageorgiou, SZ Abidi, HY Chang, XJ Li, GJ Kato, GE Karniadakis, M Dao, and S Suresh, “Simultaneous polymerization and adhesion under hypoxia in sickle cell anemia,” Proc. Natl. Acad. Sci. U.S.A. 2018, 15 (38), 9473-9478. 2018.
  21. H Li, L Lu, X Li, P. Buffet, M Dao, GE Karniadakis, and S Suresh, “Mechanics of diseased red blood cells in human spleen and consequences for hereditary blood disorders,” Proc. Natl. Acad. Sci. U.S.A., 115 (38), 9574- 9579, 2018.
  22. HY Chang, X Li, and GE Karniadakis*, “Modeling of biomechanics and biorheology of red blood cells in type-2 diabetes mellitus,” Biophys. J. 2017, 113, 481-490. (BJ Highlighted Article).
  23. X Li, E Du, M Dao, S Suresh, and GE Karniadakis, “Patient-specific modeling of individual sickle cell behavior under transient hypoxia,” PLOS Comput. Biol. 2017, 13, e1005426. (Highlighted on Biophysical Society Blog).
  24. X Li, M Dao, G Lykotrafitis, and GE Karniadakis, “Biomechanics and biorheology of red blood cells in sickle cell anemia,” J. Biomech. 2017, 50, 34-41. (Quarterly Most-downloaded Articles, as of June 2017)
  25. X Li, H Li, HY Chang, G Lykotrafitis, and GE Karniadakis, “Computational biomechanics of human red blood cells in hematological disorders,” J. Biomech. Eng. 2017, 139, 020804.
  26. Y Yoshimoto, Z Li, L Kinefuchi and GE Karniadakis, “Construction of non-Markovian coarse-grained models employing the Mori-Zwanzig formalism and iterative Boltzmann inversion,” The Journal of Chemical Physics, 2017, 147: 244110. (Selected as Editor’s Pick featured article).
  27. L Lu, H Li, X Bian, X Li, GE Karniadakis, “Mesoscopic adaptive resolution scheme: toward understanding of interactions between sickle cell fibers,” Biophysical Journal (COVER). 2017 Jul 11;113(1):48-59.
  28. A Yazdani, H Li, MR Bersi, P DiAchille, J Insley, JD Humphrey, GE Karniadakis, “Data-driven Modeling of Hemodynamics and its Role on Thrombus Size and Shape in Aortic Dissections,” Scientific Reports, 2018, 8:2515.
  29. Z Li, X Bian, YH Tang, GE Karniadakis, “A dissipative particle dynamics method for arbitrarily complex geometries,” J. Comp. Phys., 2018, 355: 534-547.
  30. Y Tang, L Lu, H Li, C Evangelinos, L Grinberg, V Sachdeva, GE Karniadakis, “OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution,” Biophysical Journal, 2017, 112:2030-2037.
  31. AL Blumers, YH Tang, Z Li, X Li, GE Karniadakis, “GPU-accelerated red blood cells simulations with transport dissipative particle dynamics,” Computer Physics Communications, 2017, 217, pp.171-179., 2017.
  32. M Deng, W Pan, GE Karniadakis, “Anisotropic single-particle dissipative particle dynamics model,” J. Comp. Phys. 2017, 336; 481-491.
  33. A Yazdani, H Li, JD Humphrey, GE Karniadakis, “A General Shear-Dependent Model for Thrombus Formation,” PLoS Comput Biol. 13(1): e1005291, 2017. doi:10.1371/journal.pcbi.1005291.
  34. Z Li, HS Lee, E Darve, GE Karniadakis, “Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts,” J. Chem. Phys. 2017, 146, DOI:10.1063/1.4973347
  35. X Li, GE Karniadakis, “Biomechanics and biorheology of red blood cells in sickle cell anemia,” J. Biomechanics, 50: 34-41, 2017.
  36. H Chang, X Li, H Li, GE Karniadakis, “MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease,” PLOS Computational Biology, 2016, 12(10), e1005173, 2016.
  37. H Lei, GE Karniadakis, “Systematic parameter inference in stochastic mesoscopic modeling,” J. Comp. Phys., 330: 571-593, 2017.
  38. MK Rausch, GE Karniadakis, JD Humphrey, “Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach,” Biomech Model Mechanobiol, 2016. DOI10.1007/s10237- 016-0814-1.
  39. C Kim and GE Karniadakis, “Brownian Motion of a Rayleigh Particle Confined in a Channel: A Generalized Langevin Equation Approach,” Journal of Statisical Physics, 158, 1100-1125, 2015.
  40. X Bian, M Deng, YH Tang and GE Karniadakis, “Analysis of hydrodynamic fluctuations in heterogeneous adjacent multidomains in shear flow,” Physical Review E, 93(3), 033312, 2016.
  41. X Bian, C Kim and GE Karniadakis, “111 years of Brownian motion,” Soft Matter, to appear, 2016.
  42. X Bian, Z Li and GE Karniadakis, “Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition,” J. Comput. Phys., 297, 131-155, DOI:10.11016/jjcp.2015.04.044, 2015.
  43. P Perdikaris, L Grinberg and GE Karniadakis, “Multiscale modeling and simulation of brain blood flow,” Phys. of Fluids, 28, 021304, DOI: 10/1063/1.4941315, 2016.
  44. A Yazdani, M Deng, B Caswell and GE Karniadakis, “Flow in complex domains simulated by Dissipative Particle Dynamics driven by geometry-specific body-forces,” 305, 906-920, doi:10.1016/j.jcp.2015.11.001 2016.
  45. A Witthoft, A Yazdani, Z Peng, C Bellini, JD Humphrey and GE Karniadakis, “A discrete particle model of a multilayered fiber-reinforced arterial wall,” J. Roy. Soc. Interface, 13, 20150964, DOI: 10.1098/rsif.2015.0964, 2016.
  46. A Yazdani and GE Karniadakis, “Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction,” Soft Matter, 12, 4339, DOI:10.1039/c6bsm00154h, 2016.
  47. XJ Li, E Du, H Lei, YH Tang, M Dao, S Suresh and GE Karniadakis, “Patient-specific modeling and predicting blood viscosity in sickle-cell anemia,” Interface Focus, 6, 20150065, DOI: 10.1098/rsfs.2015.0065m 2016.
  48. YH Tang, Z Li, XJ Li, MG Deng and GE Karniadakis, “Non-equilibrium dynamics of vesicles and micelles by self-assembly of block copolymers with double thermoresponsivity,” Macromolecules, 59, 2895-2903, DOI: 10.1021/acs.macromol.6600365, 2016.
  49. A Yazdani, XJ Li and GE Karniadakis, “Dynamic and rheological properties of soft biological cell suspensions,” Rheol Acta, 55(6), 433-449, DOI 10.1007/s00397-015-0869-4, 2016.
  50. L Lu, XJ Li, PG Vekilov and GE Karniadakis, “Probing the twisted structure of sickle hemoglobin fibers via particle simulations,” Biophys. J., 110, 2085-2093, doi:10.1016/j.bpj.2016.04.002, 2016.
  51. X Bian, Z Li, M Deng and GE Karniadakis, “Fluctuating hydrodynamics in periodic domains and heterogeneous adjacent multidomains: Thermal equilibrium,” Physical Review E, 92 (5), 053302, 2015.
  52. Z Li, A Yazdani, A Tartakovsky and GE Karniadakis, “Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems,” J. Chem. Phys., 143, 014101, DOI: 10.1063/1.4923254, 2015.
  53. P Perdikaris, L Grinberg and GE Karniadakis, “An effective fractal-tree closure model for simulating blood flow in large arterial networks,” Annals. Biomed. Engin., 43(6), 1432-1442, DOI: 10.1007/s10439-014-1221-3, 2015.
  54. Z Li, X Bian, X Li and GE Karniadakis, “Incorporation of memory effects in coarse-grained modeling via the Mori-Zwanzig formalism,” J. Chem. Phys. 143, 243128, DOI: 10.1063/1.4935490, 2015.
  55. Z Li, YH Tang, X Li and GE Karniadakis, “Mesoscale modeling of phase transition dynamics of thermoresponsive polymers,” Chem. Commun. 51, 11038-11040, DOI: 10.1039/c5cc01684c, 2015.
  56. M Deng and GE Karniadakis, “Electrostatic correlations near charged planar surfaces,” J. Chem. Phys. 141, 094703, DOI: 10.1063/1.3894053, 2014.
  57. Z Li, X Bian, B Caswell and GE Karniadakis, “Construction of dissipative particle dynamics models for complex fluids via the Mori-Zwannzig formulation,” Soft Matter, DOI: 10.1039/C4SM01387E, 2014.
  58. Z Li, YH Tang, H Lei, B Caswell and GE Karniadakis, “Energy-conserving dissipative particle dynamics with temperature-dependent properties,” J. Comput. Phys., 265, 113-127, 2014.
  59. K Lykov, X Li, H Lei, IV Pivkin and GE Karniadakis “Inflow/outflow boundary conditions for particle-based blood flow simulations: Application to arterial bifurcations and trees,” PLOS Computational Biology, 11 e1994419, DOI:10.1371/journal.pcbi.1004410, August 28, 2015.
  60. M Deng, L Grinberg, B Caswell and GE Karniadakis, “Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow,” Soft Matter, 11, 4962-4972, DOI: 10.1039/C4SM02395A, 2015.
  61. X Li, Z Peng, H Lei, M Dao and GE Karniadakis, “Probing red blood cell mechanics, rheology and dynamics with a two-component multiscale model,” Ph. Trans. R. Soc. A, 372, 20130389, DOI: 10.198/rsta.2013.0389, 2014.
  62. DA Fedosov*, M Dao, GE Karniadakis and S Suresh, “Computational biorheology of human blood flow in health and disease,” Annals of Biomedical Engineering, 42(2), 368-387, February 2014.
  63. M Deng* and GE Karniadakis, “Electrostatic correlations near charged planar surfaces,” The Journal of Chemical Physics 141(9):094703. DOI: 10.1063/1.4894053, 2014.
  64. Z Li, X Bian, B Caswell, and GE Karniadakis, “Construction of dissipative particle dynamics models for complex fluids via the Mori-Zwanzig formulation,” Soft Matter, 10 (43), 8659-8672. DOI: 10.1039/C4SM01387E, 2014.
  65. C Kim* and GE Karniadakis. “Brownian motion of a Rayleigh particle confined in a channel: A generalized Langevin equation approach,” Journal of Statistical Physics, 10.1007/s10955-014-1160- 2, 2014.
  66. X Li, YH Tang*, HJ Liang, and GE Karniadakis, “Large-scale dissipative particle dynamics simulations of self-assembled amphiphilic systems,” Chem. Commun. 2014, 50, 8306-8308.
  67. C Kim* and GE Karniadakis, “Time correlation functions of Brownian motion and evaluation of friction coefficient in the near-Brownian-limit regime,” Multiscale Model. Simul., vol. 12, 225-248, 2014.
  68. X Li, Z Peng, H Lei*, M Dao and GE Karniadakis, “Probing red cell mechanics, rheology and dynamics with a two-component multiscale model,” Phil. Trans. Royal Society A, 372, 20130389, 2014.
  69. M Deng* and GE Karniadakis, “Coarse-grained modeling of protein unfolding dynamics,” Multi- scale Model. Simul., vol. 12, pp. 109-118, 2014.
  70. P Perdikaris* and GE Karniadakis, “Fractional-order viscoelasticity in one-dimensional blood flow models,” Annals of Biomedical Engineering, vol. 42(5), pp. 1012-1023, 2014.
  71. D Fedosov*, M Dao, GE Karniadakis and S Suresh, “Computational biorheology of human blood flow in health and disease,” Annals of Biomedical Engineering, 42:368-387, 2014.
  72. Z Li, Y Tang, H Lei, B Caswell and GE Karniadakis, “Energy-conserving dissipative particle dynamics with temperature-dependent properties,” J. Comp. Phys., 265:113-127, 2014.
  73. A Witthoft*, JA Filosa and GE Karniadakis, “Potassium buffering in the neurovascular unit: Models and sensitivity analysis,” Biophysical Journal, 105, 2046-2054, 2013.
  74. Z Peng, X Li, I Pivkin, M Dao, GE Karniadakis, and S Suresh “Lipid bi-layer and cytoskeletal interactions in a red blood cell,” Proc. Nat. Acad. Sciences, 110(33):13356-61, 2013.
  75. X Li, P Vlahovska and GE Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red cells in health and disease,” Soft Matter, 9:28-37, 2013.
  76. H Lei*, B Caswell and GE Karniadakis, “Blood flow in small tubes: Quantifying the transition to the non-Newtonian regime,” J. Fluid Mechanics, 722:214-239, 2013.
  77. H Lei* and GE Karniadakis, “Probing vaso-occlusion phenomena in sickle cell anemia via mesoscopic simulations,” Proc. Nat. Acad. Sciences, 110(28):11326-30, 2013.
  78. L Grinberg, DA Fedosov and GE Karniadakis, “Parallel multiscale simulations of a brain aneurysm,” J. Comp. Phys., 244, 131-147, 2013.
  79. C Kim* and GE Karniadakis, “Microscopic theory of Brownian motion revisited: The Rayleigh model,” Phys. Rev. E, vol. 87, 032129, 2013.
  80. M Deng*, X Li, H Liang, B Caswell and GE Karniadakis, “Simulation and modeling of slip flow over surface grafted with polymer brushes and glycocalyx fibers,” J. Fluid Mech., vol. 711, 192-211, 2012.
  81. X Li, B Caswell and GE Karniadakis, “Effect of chain chirality on the self-assembly of sickle hemoglobin,” Biophys. J., vol. 103, pp. 1130-1140, 2012.
  82. DA Steinman et al., “Variability of Computational Fluid Dynamics Solutions for pressure and flow in a giant aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge,” J. Biomechanical Engineering, 135(2):0210161:13.
  83. X Li, A Popel and GE Karniadakis, “Blood-plasma separation in Y-shaped bifurcating microfluidic channels: A dissipative particle dynamics simulation study,” Physical Biology, vol. 9, p. 026010, 2012.
  84. H Lei* and GE Karniadakis, “Predicting the morphology of sickle red blood cells using coarse-grained models of intracellular aligned hemoglobin polymers,” Soft Matter, vol. 8, p. 4507-4516, 2012.
  85. H Lei* and GE Karniadakis, “Quantifying the rheological and hemodynamic characteristics of sickle cell anemia,” Biophysical Journal, vol. 102, pp. 185-194, 2012.
  86. D Fedosov*, B Caswell, G Karniadakis, “Wall shear stress-based method for adhesive dynamics of red blood cells in malaria,” Biophysical Journal, vol. 100, pp. 2084-2093, 2011.
  87. D Fedosov, H Lei, B Caswell, S Suresh and GE Karniadakis, “Multiscale modeling of red blood cell mechanics and blood flow in malaria,” PLoS Computational Biology, vol. 7 (12), pp. 1-13, 2011.
  88. D Fedosov, W Pan, B Caswell, G Gompper and GE Karniadakis, “Predicting human blood viscosity in silico,” Proc. Nat. Acad. Sciences, vol. 108, pp. 11772-11777, 2011.
  89. W Pan, D Fedosov, B Caswell, and GE Karniadakis, “Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells,” Microvascular Research, vol. 82, pp. 163-170, 2011.
  90. H Lei, D Fedosov, and GE Karniadakis, “Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics,” J. Comp. Phys., vol. 230, pp. 3765-3779, 2011.
  91. M Arienti, W Pan*, X Li, and GE Karniadakis, “Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions,” J. Chem. Phys., vol. 134, p. 204114, 2011.
  92. D Fedosov*, B Caswell, S Suresh and GE Karniadakis, “Quantifying the biophysical characteristics of Plasmododiumfalciparum-parasitized red blood cells in microcirculation,” Proc. Nat. Acad. Sciences, vol. 108, pp. 35-39, 2011.
  93. D Quinn, I Pivkin, SY Yong, KH Chiam, M Dao, GE Karniadakis and S Suresh, “Combined simulation and experimental study of large deformation of red blood cells in microfluidic systems,” Annals of Biomedical Engineering, vol. 39(3), pp. 1041-1050, 2011.
  94. T Anor, L Grinberg*, H Baek, M Jayraman, JR Madsen and GE Karniadakis, “Modeling of blood flow in arterial trees,” Wiley Interdisciplinary Reviews: Systems Biology and Medicine, vol. 2, pp. 612-623, 2010.
  95. L Grinberg, E Cheever, T Anor, JR Madsen and GE Karniadakis, “Modeling blood flow circulation in intracranial arterial networks: A comparative 3D/1D simulation study,” Annals of Biomedical Engineering, vol. 39, pp. 297-309, 2010.
  96. H Baek*, MV Jayaraman, PD Richardson and GE Karniadakis, “Flow instability and wall shear stress variation in intracranial aneurysms,” J. of the Royal Society Interface, vol. 7, pp. 967-988, 2010.
  97. D Fedosov*, B Caswell, A Popel and GE Karniadakis, “Blood flow and cell-free layer in microvessels,” Microcirculation, vol. 17 (8), pp. 615-628, 2010.
  98. L Grinberg* and GE Karniadakis, “Extrapolation-based acceleration of iterative solvers: Application to simulation of 3D flows,” Commun. Comput. Phys., vol. 9, pp. 607-626, 2011.
  99. W Pan*, B Caswell and GE Karniadakis, “A low-dimensional model for the red blood cell,” Soft Matter, vol. 6, pp. 4366-4376, 2010.
  100. D Fedosov*, B Caswell and GE Karniadakis, “Systematic coarse-graining of spectrin-level red blood cell models,” Computer Methods in Applied Mechanics and Engineering, vol. 199, pp. 1937-1948, 2010.
  101. D Fedosov*, B Caswell and GE Karniadakis, “A multiscale red blood cell model with accurate mechanics, rheology and dynamics,” Biophysical Journal, vol. 98, pp. 1-11, 2010.
  102. H Lei*, B Caswell and GE Karniadakis, “Direct construction of mesoscopic models from microscopic simulations,” Phys. Rev. E, vol. 81(2), 026704, 2010.
  103. W Pan*, B Caswell and GE Karniadakis, “Rheology, Microstructure and Migration in Brownian Colloidal Suspensions,” Langmuir, vol. 26(1), pp. 133-142, 2010.
  104. H Baek*, MV Jayaraman and GE Karniadakis, “Wall shear stress and pressure distribution on aneurysms and mesoscopic in the posterior communicating artery bifurcation,” Annals of Biomedical Engineering, Vol. 37, No. 12, pp. 2469-2487, 2009.
  105. I Pivkin*, P Richardson and GE Karniadakis, “Effect of red blood cells on platelet aggregation,” IEEE Engineering in Medicine Biology Magazine, vol. 28(2), 32-37, March-April 2009.
  106. L Grinberg*, A Yakhot and GE Karniadakis, “Analyzing transient turbulence in a stenosed artery by Proper Orthogonal Decomposition,” Annals of Biomedical Engineering, vol. 37(1), pp. 2200-2217, 2009.
  107. X Li, I Pivkin*, H Liang and GE Karniadakis, “Shape transformations of membrane vesicles from amphiphilic triblock copolymers: A Dissipative Particle Dynamics simulation study,” Macromolecules, vol. 42, pp. 3195-3200, 2009.
  108. J Foo*, S Sindi and GE Karniadakis, “Multi-element probabilistic collocation for sensitivity analysis in cellular signaling networks,” IET Systems Biology, vol. 3 (4), pp. 239-254, 2009.
  109. D Fedosov* and GE Karniadakis, “Triple-Decker: Interfacing atomistic-mesoscopic-continuum flow regimes,” J. Comp. Phys., vol. 228, pp. 1157-1171, 2009.
  110. L Grinberg*, T Anor, E Cheeve, JR Madsen and GE Karniadakis, “Simulation of the Human Intracranial Arterial Tree,” Philosophical Transactions of the Royal Society A, vol. 367, pp. 2371- 2386, 2009.
  111. W Pan, DA Fedosov, B Caswell and GE Karniadakis, “Hydrodynamic interactions for single dissipative-particle dynamics particles and their clusters and filaments,” Phys. Rev. E, vol. 78, 046706, 2008.
  112. W Pan, IV Pivkin, and GE Karniadakis, “Single-particle hydrodynamics in DPD: A new formulation,” EuroPhysics Letters, vol. 84, 10012, 2008.
  113. L Grinberg* and GE Karniadakis, “Outflow boundary conditions for arterial networks with multiple outlets,” Annals of Biomedical Engineering, vol. 36 (9), pp. 1496-1514, 2008.
  114. L Grinberg*, T Anor, JR Madsen, A Yakhot and GE Karniadakis, “Large-Scale Simulation of the Human Arterial Tree,” Clinical and Experimental Pharmacology and Physiology, published on-line July 2008.
  115. I Pivkin* and GE Karniadakis, “Accurate coarse-grained modeling of red blood cells,” Phys. Rev. Let., vol. 101(11), 118105, 2008.
  116. D Fedosov*, GE Karniadakis and B Caswell, “Dissipative particle dynamics simulation of depletion layer and polymer migration in micro-and nanochannels for dilute polymer solutions,” J. Chem. Phys., vol. 128, pp. 144903-14, 2008.
  117. D Fedosov, I Pivkin, and GE Karniadakis, “Velocity limit in DPD simulations of wall-bounded flows,” J. Comp. Phys., vol. 227, pp. 2540-2559, 2008.
  118. A Yakhot, T Amor and GE Karniadakis, “A reconstruction method for gappy and noisy arterial flow data,” IEEE Transactions on Medical Imaging, vol. 26, No. 12, pp. 1681-1697, 2007.
  119. I Pivkin*, PD Richardson and GE Karniadakis, “Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi,” Proc. Nat. Acad. Sci., USA, vol. 103, no. 46, 17164, 2006.
  120. PD Richardson, I Pivkin*, GE Karniadakis, and DH Laidlaw, “Blood flow at arterial branches: Complexities to resolve at the angioplasty suite,” Lecture Notes in Computer Science, vol. 3993,
    pp. 538-545, 2006.
  121. V Symeonidis*, GE Karniadakis and B Caswell, “Schmidt number effects in dissipative particle dynamics simulation of polymers,” J. Chem. Phys., vol. 125, 184902, 2006.
  122. I Pivkin* and GE Karniadakis, “Controlling density fluctuations in wall-bounded dissipative particle dynamics systems,” Phys. Rev. Let., vol 96 (20), 206001, 2006.
  123. V Symeonidis* and GE Karniadakis, “A family of time-staggered schemes for integrating hybrid DPD models for polymers: Algorithms and applications,” J. Comp. Phys., vol. 218, pp. 82-101, 2006.
  124. I Pivkin* and GE Karniadakis, “Coarse-graining limits in open and wall-bounded DPD systems,” J. Chem. Phys., vol. 124, 184101, 2006.
  125. E Keaveny, I Pivkin*, MR Maxey and GE Karniadakis, “A comparative study between dissipative particle dynamics and molecular dynamics for simple-and complex-geometry flows,” J. Chem. Phys., vol. 123, p. 104-107, 2005.
  126. V Symeonidis*, GE Karniadakis and B Caswell, “Dissipative particle dynamics simulations of polymer chains: Scaling laws and shearing response compared to DNA experiments,” Phys. Rev. Lett., vol 95, 076001, 2005.
  127. I Pivkin*, PD Richardson, DH Laidlaw and GE Karniadakis, “Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model,” J. Biomechanics, vol. 38, pp. 1283- 1290, 2005.
  128. I Pivkin* and GE Karniadakis, “A new method to impose no-slip boundary conditions in dissipative particle dynamics,” J. Comp. Phys., vol. 207, pp. 114-128, 2005.
  129. V Symeonidis*, GE Karniadakis and B Caswell, “A seamless approach to multiscale complex fluid simulation,” Computing in Science Engineering, pp. 39-46, May/June 2005.
  130. A. Beskok* and G.E. Karniadakis, “A model for flows in channels, pipes and ducts at micro and nanoscales,” J. Microscale Thermophysical Engineering, vol. 3, pp. 43-77, 1999.
  131. A. Beskok*, G.E. Karniadakis and W. Trimmer, “Rarefaction and compressibility effects in gas microflows,” J. Fluids Engineering, vol. 118, p. 448, 1996.
  132. S.J. Sherwin*, G.E. Karniadakis S.A. Orszag, “Numerical simulation of the ion etching process,” J. Comp. Phys., vol. 110, p. 373, 1994.
  133. A. Beskok* and G.E. Karniadakis, “Simulation of heat and momentum transfer in complex microgeometries,” J. Thermophys. and Heat Transfer, vol. 8, no. 4, p. 647, 1994.
  134. M.K. Sharp, R. D. Kamm, A.H. Shapiro, E. Kimmel G.E. Karniadakis, “Dispersion in a curved tube during oscillatory flow,” J. Fluid Mech., vol. 223, p. 537, 1991.
  135. S.J. Sherwin*, E. Barough, G.E. Karniadakis S.A. Orszag, “Modeling of multilayer etching processes,” J. of Vacuum Science and Technology, vol. 11, p. 1310, 1993.

Fluid Mechanics

  1. S Cai, C Gray, GE Karniadakis, “Physics-Informed Neural Networks Enhanced Particle Tracking Velocimetry: An Example for Turbulent Jet Flow,” IEEE Transactions on Instrumentation and Measurement, 2024
  2. M Lu, C Lin, M Maxey, G Karniadakis, Z Li, “Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning,” arXiv preprint arXiv:2403, 2024.
  3. Q Cao, S Goswami, T Tripura, S Chakraborty, GE Karniadakis, “Deep neural operators can predict the real-time response of floating offshore structures under irregular waves,” Computers & Structures 291, 107228, 2024.
  4. Z Wang, D Fan, MS Triantafyllou, GE Karniadakis, “A large-eddy simulation study on the similarity between free vibrations of a flexible cylinder and forced vibrations of a rigid cylinder,” Journal of Fluids and Structures 101, 103223, 2021.
  5. D Fan, Z Wang, MS Triantafyllou, GE Karniadakis, “Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow,” Journal of Fluid Mechanics 881, 815-858, 2019.
  6. Z Wang, MS Triantafyllou, Y Constantinides, GE Karniadakis, “An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe,” Journal of Fluid Mechanics 859, 691-730, 2019.
  7. A Yakhot, Y Feldman, D Moxey, S Sherwin, GE Karniadakis, “Turbulence in a Localized Puff in a Pipe Flow, Turbulence and Combustion,” 1-24, 2019.
  8. F. Xie, X. Zheng, Y. Constantinides, M.S. Triantafyllou, and G.E. Karniadakis, “The flow dynamics of the garden-hose instability,” J. Fluid Mech., 800, pp. 595–612, 2016, doi:10.1017/jfm.2016.364, 2016.
  9. F. Xie, Y. Yu, Y. Constantinides, M.S. Triantafyllou, and G.E. Karniadakis, “U-shaped fairings suppress vortex-induced vibrations for cylinders in cross-flow,” J. Fluid Mech., 782, 300-332, 2015.
  10. Y. Yu, F. Xie, H. Yan, Y. Constantinides, O. Oakley and G.E. Karniadakis, “Suppression of vortex-induced vibrations by fairings: A numerical study,” J. Fluids and Structures, 54, 679-700, 2015.
  11. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “On the validity of the independence principle applied to the vortex-induced vibrations of a flexible cylinder inclined at 60deg,” J. Fluids and Structures, vol. 53, pp. 58-69, 2015.
  12. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows,” J. Fluids and Structures, 41(8):33- 42, 2013.
  13. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow,” J. Fluid Mech., vol. 717, pp. 361-375, 2013.
  14. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “Phasing mechanisms between the in-line and cross-flow vortex-induced vibrations of a long tensioned beam in shear flow,” Computers and Structures, 122(6):155-163, 2013.
  15. R. Bourguet, Y. Modarres-Sadeghi, G.E. Karniadakis and M.S. Triantafyllou, “Wake-body resonance of long flexible structures is dominated by counterclockwise orbits,” Phys. Rev. Lett., vol. 107, 134502, 2011.
  16. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “Lock-in of the vortex-induced vibrations of a long tensioned beam in shear flow,” J. Fluids Structures, vol. 27, pp. 838-847, 2011.
  17. R. Bourguet, G.E. Karniadakis and M.S. Triantafyllou, “Vortex-induced vibrations of a long flexible cylinder in shear flow,” J. Fluid Mech., vol. 667, pp. 342-382, 2011.
  18. H. Baek* and G.E. Karniadakis, “Suppressing vortex-induced vibrations via passive means,” J. Fluids Structures, vol. 25(5), pp. 848-866, 2009.
  19. D. Liu*, E. Keaveny, M.R. Maxey and G.E. Karniadakis, “Force coupling method for flows with ellipsoidal particles,” J. Comp. Phys., vol. 228, pp. 3559-3581, 2009.
  20. S. Dong, G.S. Triantafyllou and G.E. Karniadakis, “Elimination of vortex streets in bluff-body flows,” Phys. Rev. Let., vol 100, 204501, 2008.
  21. J.M. Dahl, F.S. Hover, M.S. Triantafyllou, S. Dong and G.E. Karniadakis, “Resonant vibrations of bluff bodies cause multivortex shedding and high frequency forces,” Phys. Rev. Let., vol 99, (14), 144503, 2007.
  22. J. Xu*, S. Dong, M.R. Maxey and G.E. Karniadakis, “Turbulent drag reduction by constant near-wall forcing,” J. Fluid Mech., vol. 582, pp. 79-101, 2007.
  23. E. Climent, K. Yeo, M.R. Maxey and G.E. Karniadakis, “Dynamic self-assembly of spinning particles,” J. Fluids Engin., vol. 129, pp. 379-387, 2007.
  24. G.V. Papaioannou, D.K.P. Yue, M.S. Triantafyllou and G.E. Karniadakis, “Three-dimensionality effects in flow around two tandem cylinders,” J. Fluid Mech., vol. 558, pp. 387-413, 2006.
  25. G.V. Papaioannou, D.K.P. Yue, M.S. Triantafyllou and G.E. Karniadakis, “Evidence of holes in the Arnoldi tongues in flow past two oscillating cylinders,” Phys. Rev. Lett., vol 96, 014501, 2006.
  26. S. Dong, G.E. Karniadakis, A. Ekmekci and D. Rockwell, “A combined DNS-PIV study of the turbulent near-wake,” J. Fluid Mech., vol. 569, pp. 185-207, 2006.
  27. D. Lucor, J. Foo, and G.E. Karniadakis, “Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping,” Journal of Fluids Structures, vol. 20(4), pp. 483-503, 2005.
  28. S. Dong and G.E. Karniadakis, “DNS of flow past a stationary and oscillating cylinder at Re = 10000,” Journal of Fluids Structures, vol. 20(4), pp. 519-531, 2005.
  29. D. Liu*, M.R. Maxey and G.E. Karniadakis, “Simulations of dynamic self-assembly of paramagnetic microspheres in confined microgeometries,” Journal of Micromechanics and Microengineering, vol. 15, pp. 2298-2308, 2005.
  30. E. Climent, M.R. Maxey and G.E. Karniadakis, “Dynamics of self-assembled chaining in magnetorheological fluids,” Langmuir, vol. 20(2), pp. 507-513, 2004.
  31. D. Liu*, M.R. Maxey and G.E. Karniadakis, “Modeling and optimization of colloidal micro-pumps,” Journal of Micromechanics and Microengineering, vol. 14, pp. 567-575, 2004. (Top 3% of downloads across all IOP journals.)
  32. S. Sirisup*, G.E. Karniadakis, N. Saelim and D. Rockwell, “DNS and experiments of flow past a wired cylinder at low Reynolds number,” European Journal of Mechanics B/Fluids, vol. 23, pp. 181-188, 2004.
  33. D. Lucor* and G.E. Karniadakis, “Effects of Oblique inflow in vortex-induced vibrations,” Flow, Turbulence and Combustion, vol. 71, pp. 375-389, 2003.
  34. X. Ma, V. Symeonidis, and G.E. Karniadakis, “A spectral vanishing viscosity method for stabilizing viscoelastic flows,” J. Non-Newtonian Fluid Mechanics, vol. 115, pp. 125-155, 2003.
  35. J. Xu*, S. Dong, M.R. Maxey and G.E. Karniadakis, “Direct numerical simulation of turbulent channel flow with bubbles,” Contemporary Mathematics, vol. 329, pp. 347-354, 2003.
  36. J. Xu*, M. Maxey and G.E. Karniadakis, “Numerical simulation of turbulent drag reduction using microbubbles,” J. Fluid Mech., vol. 468, pp. 271-281, 2002.
  37. D. Lucor, C. Evangelinos, L. Imas and G.E. Karniadakis, “Flow-induced vibrations of non-linear cables, Part II: Simulations,” Int. J. Num. Meth. Engin., vol. 55, pp. 557-571, 2002.
  38. Y. Du, V. Symeonidis, and G.E. Karniadakis, “Drag reduction in wall-bounded turbulence via a transverse traveling wave,” J. Fluid Mech., vol. 457, pp. 1-34, 2002.
  39. D. Lucor*, L. Imas and G.E. Karniadakis, “Vortex dislocations and force distribution of long flexible cylinders subjected to sheared flows,” J. Fluids Structures, vol. 15, pp. 641-650, 2001.
  40. Y. Du* and G.E. Karniadakis, “Suppressing wall turbulence by means of a transverse traveling wave,” Science, vol. 288, pp. 1230-1234, 2000.
  41. X. Ma, G.-S. Karamanos, and G.E. Karniadakis, “Dynamics and low-dimensionality in the turbulent near-wake,” J. Fluid Mech., vol. 410, pp. 29-65, 2000.
  42. C. Evangelinos, D. Lucor, and G.E. Karniadakis, “DNS-derived force distribution on flexible cylinders subject to vortex-induced vibration,” J. Fluid Mech., vol. 14(3), pp. 429-440, 2000.
  43. G.E. Karniadakis, “Simulating turbulence in complex geometries,” Fluid Dynamics Research, vol. 24 (6), pp. 343- 362, 1999.
  44. C. Evangelinos* and G.E. Karniadakis, “Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations,” J. Fluid Mech., vol. 400, pp. 91-124, 1999.
  45. D.J. Newman* and G.E. Karniadakis, “Simulations of flow past a freely vibrating cable,” J. Fluid Mech., vol. 344, p.95, 1997.
  46. C.H. Crawford* and G.E. Karniadakis, “Reynolds stress analysis of EMHD-controlled wall turbulence, Part I: Stream-wise forcing,” Phys. Fluids, vol. 9(3), 1997.
  47. D.J. Newman* and G.E. Karniadakis, “Simulations of flow over a flexible cable: A comparison of forced and flow-induced vibrations,” J. Fluids Structures, vol. 10, p. 439, 1996.
  48. L. Kaiktsis, G.E. Karniadakis and S.A. Orszag, “Unsteadiness and convective instabilities in flow over a backward-facing step,” J. Fluid Mech., vol. 321, p. 157, 1996.
  49. G.E. Karniadakis and G.L. Brown, “Vorticity transport in modeling three-dimensional unsteady shear flows,” Phys. Fluids, vol 7(4), p. 688, 1995.
  50. D. Chu* G.E. Karniadakis, “A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces,” J. Fluid Mech., vol. 250, p.1, 1993.
  51. M.V. Zagarola, A.J. Smits G.E. Karniadakis, “Heat transfer enhancement in transitional channel flow,” J. Wind Engineering Industrial Aerodynamics, vol. 49, p. 257, 1993.
  52. D. Chu, R.D. Henderson, G.E. Karniadakis, “Parallel spectral element-Fourier simulation of turbulence over ribletmounted surfaces,” Theor. Comput. Fluid Dynamics, vol. 3, p.219, 1992.
  53. A.G. Tomboulides*, G.S. Triantafyllou G.E. Karniadakis, “A new mechanism of period doubling in free shear flows,” Phys. Fluids, vol. 4 (7), p. 1329, 1992.
  54. G.E. Karniadakis G.S. Triantafyllou, “Three-dimensional dynamics and transition to turbulence in the wake of bluff objects,” J. Fluid Mech., vol. 238, p. 1, 1992.
  55. P.F. Batcho* G.E. Karniadakis, “Chaotic transport in two-and three-dimensional flow past a cylinder,” Phys. Fluids, vol. 3(5), p. 1051, 1991.
  56. D. Barkley, G.E. Karniadakis, I.G. Kevrekidis, A.J. Smits Z.H. Shen, “Chaotic advection in a complex annular geometry,” Phys. Fluids, vol. 3(5), p. 1063, 1991.
  57. L. Kaiktsis*, G.E. Karniadakis S.A. Orszag, “Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step,” J. Fluid Mech., vol. 231, p. 501, 1991.
  58. P.F. Batcho*, G.E. Karniadakis S.A. Orszag, “Numerical investigation of the spreading of self-excited stratified jets,” ASME Symp. on Unsteady Flows, Toronto, 1990, also in J.Fluids Structures, vol. 5, p. 681-700, 1991.
  59. G.S. Triantafyllou G.E. Karniadakis, “Computational reducibility of unsteady viscous flows,” Phys. Fluids, vol. 2, p. 653, 1990.
  60. G.E. Karniadakis G.S. Triantafyllou, “Frequency selection and asymptotic states in laminar wakes,” J. Fluid Mech., vol. 199, p. 447, 1989.
  61. G.E. Karniadakis G.S. Triantafyllou, “The crisis of transport measures in chaotic flow past a cylinder,” Phys. Fluids, vol. 4, p. 628, 1989.
  62. G.E. Karniadakis, B.B. Mikic A.T. Patera, “Transport enhancement by flow destabilization: Reynolds’ analogy revisited,” J. Fluid Mech., vol. 192, p. 365, 1988.
  63. G.E. Karniadakis, “Numerical simulation of forced convection heat transfer from a cylinder in crossflow,” Int. J. Heat Mass Transfer, vol. 31, p. 107, 1988.

Low-Dimensional Modeling

  1. X. Yang*, D. Venturi, C. Cheng, C. Chryssostomidis and G.E. Karniadakis, “EOF-based constrained sensor placement and field reconstruction from noisy ocean measurements: Application to Nantucket Sound,” J. Geophys. Res. Oceans, vol. 115, C12072, 2010.
  2. B. Yildirim*, C. Chryssostomidis and G.E. Karniadakis, “Efficient Sensor Placement for Ocean Measurements using Low-dimensional Concepts,” Ocean Modelling, vol. 27, pp. 160-173, 2009.
  3. S. Sirisup*, G.E. Karniadakis, D. Xiu and I.G. Kevrekidis, “Equation-free/Galerkin-free POD-assisted computation of incompressible flows,” Journal of Computational Physics, vol. 207(2), pp. 568-587, 2005.
  4. S. Sirisup*, G.E. Karniadakis, “Stability and accuracy of periodic flow solutions obtained by a POD-penalty method,” Physica D, vol. 202, pp. 218-237, 2005.
  5. S. Sirisup*, G.E. Karniadakis, “A spectral viscosity method for correcting the long-term behavior of POD models,” J. Comp. Phys., vol. 194, pp. 92-116, 2004.
  6. S. Sirisup*, G.E. Karniadakis, Y. Yang and D. Rockwell, “Wave-structure interaction: simulation driven by quantitative imaging,” Proc. R. Soc. Lond. A, vol. 460, pp. 729-755, 2004.
  7. X. Ma*, G.E. Karniadakis, H. Park and M. Gharib, “DPIV-Driven simulation: A new computational paradigm,” Proc. Royal Soc. A, vol. 459, pp. 547-565, 2003.
  8. X. Ma*, G.E. Karniadakis, H. Park and M. Gharib, “DPIV/T-Driven convective heat transfer simulation,” Int. J. Heat Mass Transfer, vol. 45, pp. 3517-3527, 2002.
  9. X. Ma* and G.E. Karniadakis, “A low-dimensional model for simulating 3D cylinder flow,” J. Fluid Mech., vol. 458, pp. 181-190, 2002.
  10. A.K. Bangia, P.F. Batcho*, I.G. Kevrekidis and G.E. Karniadakis, “Unsteady 2D flows in complex geometries: Comparative bifurcation studies with global eigenfunction expansions,” SIAM J. Sci. Stat. Comp., vol. 18, p. 775, 1997.
  11. P. F. Batcho* G.E. Karniadakis, “Generalized Stokes eigenfunctions: A new trial basis for the incompressible Navier-Stokes equations,” J. Comp. Phys., vol 115, p. 121, 1994.
  12. A.E. Deane, I.G. Kevrekidis, G.E. Karniadakis S.A. Orszag, “Low-dimensional models for complex geometry flows: Application to grooved channels and circular cylinders,” Phys. Fluids, vol. 3(10),p. 2337, 1991.

Parallel Computing

  1. A. L. Blumers, Y. Tang, Z. Li, X. Li, G. E. Karniadakis, “GPU-accelerated red blood cells simulations with transport dissipative particle dynamics,” Computer Physics Communications, 2017, http://dx.doi.org/10.1016/j.cpc.2017.03.016
  2. P. Perdikaris, J.A. Insley, L. Grinberg, Y. Yu, M. Papka and G.E. Karniadakis, “Visualizing multi-physics, fluid-structure interaction phenomena in intracranial aneuryms,” In Press: Parallel Com- puting, 55, 9-16, 2016.
  3. Y-H. Tang, S. Kudo, X. Bian, Z. Li and G.E. Karniadakis, “Multiscale universal interface: A concurrent framework for coupling heterogeneous solvers,” J. Comp. Phys., 297, 13-31, DOI: 10.1016/j.jcp.2015.05.004, 2015.
  4. Y.-H. Tang and G.E. Karniadakis, “Accelerating Dissipative Particle Dynamics Simulations on GPUs: Algorithms, Numerics and Applications,” Comput. Phys. Commun., 185, 2809-2822, 2014.
  5. L. Grinberg, D. Fedosov and G. E. Karniadakis, “Parallel multiscale simulations of a brain aneurysm,” Journal of Computational Physics, 244:131-147, 2013.
  6. L. Grinberg, J. Insley, D. Fedosov, V. Morozov, M. Papka and G. E. Karniadakis, “Tightly Coupled Atomistic-continuum Simulations of Brain Blood Flow on Petaflop Supercomputers, Computing in Science and Engineering,” vol. 14(6), p. 58-67, 2012.
  7. L. Grinberg* and G.E. Karniadakis, “A new domain decomposition method with overlapping patches for ultrascale simulations: Application to biological flows,” J. Comp. Phys., vol. 229, pp. 5541-5563, 2010.
  8. L. Grinberg*, D. Pekurovsky, S. Sherwin and G. E. Karniadakis, “Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements,” Parallel Computing, vol. 35, pp. 284- 304, 2009.
  9. L. Grinberg* and G.E. Karniadakis, “A scalable domain decomposition method for ultra-parallel arterial flow simulations,” Commun. Comput. Phys., vol. 4, pp. 1151-1169, 2008.
  10. S. Dong, J. Insley, N.T. Karonis, M. Papka, J. Binns and G.E. Karniadakis. “Simulating and visualizing the human arterial system on the TeraGrid,” Future Generation Computer Systems, The International Journal of Grid Computing: Theory, Methods and Applications, vol. 22, pp. 1011-1017, 2006.
  11. S. Dong, G.E. Karniadakis and N. Karonis, “Cross-Site Computations on the TeraGrid,” Computing in Science Engineering, vol. 7(5), 14-23, 2005.
  12. S. Dong and G.E. Karniadakis, “Dual-level parallelism for high-order CFD methods,” Parallel Computing, vol. 30(1), pp. 1-20, 2004. (Ten most downloaded articles in Parallel Computing).
  13. S. Dong and G.E. Karniadakis, “Multilevel parallelization models in CFD,” Journal of Aerospace Computing, Information and Communication, vol. 1, pp. 256-268, 2004.
  14. J.S. Sobel, A.S. Forsberg, D.H. Laidlaw, R.C. Zelesnik, D.F. Keefe, I. Pivkin*, G.E. Karniadakis, P. Richardson, S. Swartz, “Particle Flurries”, IEEE Computer Graphics and Applications, vol. 24(2), pp. 76-85, 2004.
  15. S. Dong and G.E. Karniadakis, “P-refinement and P-threads,” Comput. Methods Appl. Mech. Engrg., vol. 192, pp. 2191-2201, 2003.
  16. C. Evangelinos*, S.J. Sherwin and G.E. Karniadakis, “Parallel DNS algorithms on unstructured grids,” Comp. Meth. Appl. Mech. Engr., vol. 184, pp. 401-425, 2000.
  17. C. Evangelinos* and G.E. Karniadakis, “Parallel CFD Benchmarks on Cray Computers,” Parallel Algorithms and Applications, vol. 9, p. 273, 1996, also in Proc. Int. Conf. Parallel Algorithms, October 1995, Wuhan, China (invited presentation).
  18. C.H. Crawford, C. Evangelinos, D.J. Newman* and G.E. Karniadakis, “Parallel benchmarks of turbulence in complex geometries,” Computers and Fluids, vol. 25, p. 677, 1996, also in Proc. Parallel CFD’95, June 26-29, 1995, Pasadena, CA.
  19. P. Fischer, L.W. Ho, G.E. Karniadakis, E.M. Ronquist A.T. Patera, “Recent advances in parallel spectral element simulation of unsteady incompressible flows,” Comp. Structures, vol. 30, p. 217, 1988.

Articles in Proceedings (Referred/Invited Papers or Extended Abstracts of Papers Were Referred)

  1. Rossinelli, D., Tang, Y.-H., Lykov, K., Alexeev, D., Bernaschi, M., Hadjidoukas, P., Bisson, M., Joubert, W., Conti, C., Karniadakis G., Fatica, M., Pivkin, I., Koumoutsakos, P, ”The In-Silico Lab-on-a-Chip: Petascale and High-Throughput Simulations of Microfluidics at Cell Resolution,” ACM 2015 Gordon Bell Award Finalist, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. 2015.
  2. L. Grinberg, M. Deng, H. Lei, J. A. Insley and G. E. Karniadakis, “Multiscale Simulations of Blood-Flow: From a Platelet to an Artery,” In Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the extreme to the campus and beyond (XSEDE), Chicago, IL. (2012).
  3. J. A. Insley, L. Grinberg, M. E. Papka, “Visualization of Multiscale Simulation Data: Brain Blood Flow,” TeraGrid 11 Conference, Salt Lake City, UT, (2011).
  4. L. Grinberg*, V. Morozov, D. Fedosov, J. Insley, M.E. Papka, K. Kumar, and G.E. Karniadakis, “A new Computational Paradigm in Multiscale Simulations: Application to Brain Blood Flow,” In Proceedings of the 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC’11. (Gordon Bell Prize finalist) (2011).
  5. L. Grinberg* and G.E. Karniadakis, “Parallel Paradigm for Ultraparallel Multi-Scale Brain Blood Flow Simulations,” Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, (2011).
  6. J. A. Insley, L. Grinberg, M. E. Papka, “Visualizing Multiscale Simulation Data: Brain Blood Flow,” Proceedings of IEEE Symposium on Large-Scale Data Analysis and Visualization, Providence, RI, (2011).
  7. Z. Zhang, M. Choi, and G.E. Karniadakis, “Anchor points matter in ANOVA decomposition,” Proceedings of ICOSAHOM’09, Springer, eds. E. Ronquist J. Hesthaven, 2010.
  8. M. Milosevic-Marden, P. Prempraneerach, J. Kirtley, G.E. Karniadakis, and C. Chryssostomidis, “An end-to-end simulator for the all-electric-ship MVDC integrated power system,” Proceedings of Grand Challenges in Modeling Simulation, Simulation Multi-Conference, July 2010, Ottawa, Canada.
  9. X. Luo, B. Epps, C. Chryssostomidis and G.E. Karniadakis, “Comparison of turbulence models for simulating flow in waterjets,” Proceedings of 11th International Conference on Fast Sea Transportation, 26-29 September 2011, Honolulu, Hawaii.
  10. X. Luo, C. Chryssostomidis and G.E. Karniadakis, “Spectral element/Smoothed profile method for turbulent flow simulations of waterjet propulsion systems,” Proceedings of Grand Challenges in Modeling Simulation, Simulation Multi-Conference, July 2010, Ottawa, Canada.
  11. X. Luo, C. Chryssostomidis and G.E. Karniadakis, “Fast 3D flow simulations of a waterjet propulsion system,” Proceedings of International Simulation Multi-Conference, July 2009, Istanbul, Turkey.
  12. P. Prempraneerach, J. Kirtley, C. Chryssostomidis, M. Triantafyllou, and G.E. Karniadakis, “Design of the all-electric ship: focus on integrated power system coupled to Hydrodynamics,” Proceedings of the Electric Ship Design Symposium: Back to the Future,” presented by the Society of Naval Architects and Marine Engineers (SNAME) and the American Society of Naval Engineers (ASNE); National Harbor, MD, February 12-13, 2009.
  13. G. Lin and G.E. Karniadakis, “Stochastic Simulations and Sensitivity Analysis of Plasma Flow,” AIAA 2008-1073, 46th Aerospace Sciences Meeting Exhibit, Reno, NV, January 7-10, 2008.
  14. X. Wan and G. E. Karniadakis, “Recent advances in polynomial chaos methods,” Proceedings of the Applied Vehicle Technology Panel (AVT) Symposium: Computational Uncertainty in Military Vehicle Design (NATO/PfP Unclassified), 3-6 December 2007, Greece, Athens.
  15. H. Baek, M.V. Jayaraman, and G.E. Karniadakis, “Distribution of WSS on the internal carotid artery with an aneurysm: A CFD sensitivity study,” ASME Proceedings, IMECE2007, 11-15 November, Seattle, WA., 2007.
  16. S. Dong, N.T. Karonis and G.E. Karniadakis. “Grid solutions for biological and physical cross-site simulations on the TeraGrid,” In Proceedings of 20th IEEE International Parallel and Distributed Processing Symposium (IPDPS’06), Rhodes Island, Greece, April 2006.
  17. B. Boghosian, P. Coveney, S. Dong, L. Finn, S. Jha, G.E. Karniadakis and N.T. Karonis. “Nektar, SPICE and Vortonics: Using Federated Grids for Large Scale Scientific Applications,” Workshop on Challenges of Large Applications in Distributed Environments (CLADE), in conjunction with 15th International Symposium on High Performance Distributed Computing (HPDC-15), Paris, France, June 2006.
  18. G. Lin*, C.-H. Su and G.E. Karniadakis, “Modeling uncertainties in supersonic flow past a wedge,” 44th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 9-12, 2006.
  19. G. Lin*, C.-H. Su and G.E. Karniadakis, “Stochastic solvers for the Euler equations,” 43rd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 10-13, 2005.
  20. X. Wan* and G.E. Karniadakis, “Simulation of heat transfer with uncertainty,” Proc. of HT2005, ASME Summer Heat Transfer Conference, San Francisco, CA, July 17-22, 2005.
  21. I. Pivkin*, E. Hueso, R. Wienstein, D.H. Laidlaw, S. Swartz and G.E. Karniadakis, “Simulation and visualization of airflow around bat wings during flight,” International Conference on Computational Science (2), pp. 689-694, 2005.
  22. E. Hueso, I. Pivkin*, S. Swartz, D.H. Laidlaw, G.E. Karniadakis and K. Breuer, “Visualization of vortices in simulated airflow around bat wings during flight,” IEEE Visualization, 2004.
  23. J. Xu*, S. Dong, M.R. Maxey and G.E. Karniadakis, “Wall-slippage effect in microbubble drag reduction,” 2nd International Symposium on Seawater Drag Reduction, Busan, Korea, May 23-26, 2005.
  24. S. Dong, J. Xu*, M.R. Maxey and G.E. Karniadakis, “Microbubble dynamics in turbulent channel flow,” 2nd International Symposium on Seawater Drag Reduction, Busan, Korea, May 23-26, 2005.
  25. M.R. Maxey, D. Liu*, S. Dong and G.E. Karniadakis, “New advances in Force-Coupling Method: from Micro to Macro,” IUTAM Symposium on Computational Approaches to Disperse Multiphase Flow, Argonne, Illinois, 4-7 October, 2004.
  26. I.V. Pivkin*, P.D. Richardson and G.E. Karniadakis, “Simulation of mural platelet aggregation,” In BMES 2004 Annual Fall Meeting, Philadelphia, PA, October 2004.
  27. D. Lucor*, C.-H. Su and G.E. Karniadakis, “Karhunen-Loeve representation of periodic second-order autoregressive processes,” International Conference on Computational Science, Krakow, Poland, June 6-9, 2004.
  28. X. Wan, D. Xiu, and G.E. Karniadakis, “Modeling uncertainty in three-dimensional heat transfer problems,” Heat Transfer Conference, Lisbon, Portugal, March 24-26, 2004.
  29. M.R. Maxey, D. Liu*, G.E. Karniadakis and E. Climent, “Self-assembled particle structures for microflow systems,” Paper No. K02, Proc. 5th International Conference on Multiphase Flow, ICMF’04, Yokohama, Japan, May 30-June 4, 2004.
  30. M.R. Maxey, J.Xu*, S. Dong and G.E. Karniadakis, “Simulation Results for Microbubbles and Turbulent Drag Reduction,” Proceedings of FEDSM’03, 4th ASME-JSME Joint Fluids Engineering Conference, Honolulu, Hawaii, July 6-11 2003.
  31. D. Lucor, J. Foo, and G.E. Karniadakis, “Correlation length and force phasing of a rigid cylinder subject to VIV,” IUTAM Symposium on Integrated Modeling of Fully Coupled Structure Interactions Using Analysis, Computations and Experiments, Eds. H. Benaroya and T. Wei, Kluwer Academic Publishers, p. 187, 2003.
  32. J. Xu*, M.R. Maxey, and G.E. Karniadakis, “DNS of Turbulent Drag Reduction Using Microbubbles,” AIAA2003- 1280, 41st Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 6-9 2003.
  33. D. Lucor, X. Ma, M.S. Triantafyllou and G.E. Karniadakis, “Vortex-induced Vibrations on Long Marine Risers in Sheared Flows: DSN Studies,” Proceedings of FEDSM’03, 4th ASME-JSME Joint Fluids Engineering Conference, Honolulu, Hawaii, July 6-11 2003.
  34. D. Liu*, M.R. Maxey and G.E. Karniadakis, “FCM-Spectral Element Method for Simulating Colloidal Micro-Devices,” 2nd MIT Conference on Computational Fluid and Solid Mechanics, edited by K.J. Bathe, June 17-20 2003.
  35. Z. Yosibash, R.M. Kirby*, K. Myers, B. Szabo, G.E. Karniadakis, “High-order Finite Elements for Fluid-Structure Interaction Problems,” 4th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, April 7-10 2003, Norfolk, Virginia.
  36. D. Lucor* and G.E. Karniadakis, “Predictability and Uncertainty in Flow-Structure Interactions,” Proceedings of the Third Conference on Bluff Body Wakes and Vortex-Induced Vibrations, Port Douglas, Australia, December 2002.
  37. S. Sirisup and G.E. Karniadakis, “Direct numerical simulation of flow past a wired cylinder”, Pro- ceedings of the Third Conference on Bluff Body Wakes and Vortex-Induced Vibrations, Port Dou- glas, Australia, December 2002.
  38. S. Dong and G.E. Karniadakis, “Dual Level Parallelism for Deterministic and Stochastic CFD Problems,” Proceedings of Supercomputing 2002, Baltimore, November 2002.
  39. D. Xiu* and G.E. Karniadakis, “Modeling Uncertainty of Elliptic Partial Differential Equations via Generalized Polynomial Chaos,” Proceedings of the 5th ASCE Engineering Mechanics Division Conference, Columbia University, New York City, June 2002.
  40. D. Xiu* and G.E. Karniadakis, “Uncertainty Modeling of Burgers’ Equation by Generalized Polynomial Chaos,” Proceedings of the 4th International Conference on Computational Stochastic Mechanics, Corfu, Greece, June 2002.
  41. I. Pivkin*, D.H. Laidlaw, P. Richardson and G.E. Karniadakis, “Moving meshes and flow simulations in coronary arteries,” Proceedings of the 8th International Conference on Numerical Grid Generation in Computational Field Simulations, p. 467, Honolulu, Hawaii, June 2002.
  42. J. Sobel, A.S. Forsberg, P. Richardson, D.H. Laidlaw, D.F. Keefe, I. Pivkin* and G.E. Karniadakis, “Arterial flows seen in virtual reality,” Proceedings of the 21st Southern Biomedical Engineering Conference, pp. 349-350, 2002.
  43. I. Pivkin, R.M. Kirby and G.E. Karniadakis, “High-order discontinuous Galerkin methods: Simulation of COIL flows,” Proc. Third AFOSR DNS/LES Conference, 2001.
  44. G. Lin* and G.E. Karniadakis, “A High-order discontinuous Galerkin method for modeling micro pulsed plasma thrusters,” Proc. International Electric Propulsion Conference, Pasadena, CA, 2001.
  45. D. Liu*, M. Maxey and G.E. Karniadakis, “A fast algorithm for particulate microflows in complex geometries,” Proc. ASME, November 2001.
  46. B. Pulvirenti, X. Ma* and G.E. Karniadakis, “A POD-based nonlinear Galerkin method for flow-thermal problems,” Proc. ECCOMAS, September 2001.
  47. D. Lucor, D. Xiu and G.E. Karniadakis, “Modeling uncertainty in flow-structure interactions,” Proc. First MIT Conference, June 2001.
  48. D. Lucor, C. Evangelinos and G.E. Karniadakis, “DNS-derived force distribution on flexible cylinders subject to VIV with shear inflow,” Proc. in Flow Induced Vibration, eds. Ziada Staubli, Bakelma, Rotterdam, 2000.
  49. R.M. Kirby, Y. Du, D. Lucor, X. Ma, G.-S. Karamanos and G.E. Karniadakis, “Parallel DNS and LES of turbulence and flow-structure interactions,” Proceedings of the DoD HPCMP Users Group Conference, June 5-8, 2000.
  50. A. Forsberg, R.M. Kirby*, D.H. Laidlaw, G.E. Karniadakis, A. van Dam and J. Elion, “Immersive virtual reality for visualizing flow through an artery,” Proc. IEEE Visualization 2000, Salt Lake City, UT, October 2000.
  51. G.-S. Karamanos, C. Evangelinos, R. Boes, R.M. Kirby and G.E. Karniadakis, “DNS of turbulence on a PC/Linux cluster: Fact or Fiction?,” Proc. SuperComputing 1999.
  52. R.M. Kirby, I. Lomtev, C. Evangelinos*, G.-S. Karamanos and G.E. Karniadakis, “Parallel DNS of flow-structure interactions,” Proceedings of the DoD HPCMP Users Group Conference, June 7-10, 1999.
  53. I. Lomtev, R.M. Kirby, and G.E. Karniadakis, “A discontinuous Galerkin method in moving domains,” In Proc. of Discontinuous Galerkin Methods: Theory, Computation and Applications, eds. Cockburn et al. , Springer-Verlag, NY, 1999.
  54. I. Lomtev, R.M. Kirby, and G.E. Karniadakis, “DNS for flow past a 3D flexible wing,” Proc. of Second AFOSR Conference, Rutgers, June 7-9, 1999, published by Kluwer, eds. D. Knigh L. Sakell.
  55. R.M. Kirby, T.C. Warburton, S.J. Sherwin, A. Beskok and G.E. Karniadakis, “The Nektar Code: Dynamic Simulations without Remeshing,” Proc. 2nd International Conference on Compu- tational Technologies for Fluid/Thermal/Chemical Systems with Industrial Applications, August 1-5, 1999.
  56. X. Ma, G.E. Karniadakis, G. Karamanos and S.J. Sherwin, “Issues in LES of wake flows,” AIAA 98-2893, 29th AIAA Fluid Dynamics Conference, Albuquerque, NM, June 15-18, 1998.
  57. T.C. Warburton, I. Lomtev, R.M. Kirby*, and G.E. Karniadakis, “A discontinuous Galerkin method for the compressible Navier-Stokes equations on hybrid grids,” Proc. Tenth International Conference on Finite Elements in Fluids, January 5-8, 1998, Tucson, Arizona, p. 604, Eds. M. Hafiz and J.C. Heinrich.
  58. H. Marmanis, Y. Du, C.H. Crawford*, and G.E. Karniadakis, “Turbulence control via geometry modifications and electromagnetic fields,” Proc. ECCOMAS 98, Athens, Greece, 1998.
  59. C.H. Crawford, H. Marmanis, and G.E. Karniadakis, “The Lamb vector and its divergence in turbulent drag reduction,” Proc. Int. Symposium on Seawater Drag Reduction, Newport, RI, July 22-24, 1998.
  60. Y. Du, C.H. Crawford, and G.E. Karniadakis, “Lorentz force modeling in EMHD turbulence control: DNS studies,” Proc. Int. Symposium on Seawater Drag Reduction, Newport, RI, July 22-24, 1998.
  61. C.E. Evangelinos* and G.E. Karniadakis, “Correlation length and forces in flow past a freely-oscillating cylinder,” Proc. ASME Fluids Engineering Division Summer Meeting, eds. P. Bearman and C.H.K. Williamson, Washington DC, June 21-25, 1998.
  62. H.F. Liu, N. Gatsonis, A. Beskok and G.E. Karniadakis, Simulation models for rarefied flow past a sphere in a pipe,” Proc. 21st Symposium on Rarefied Gas Dynamics, France, 1998.
  63. X. Ma* and G.E. Karniadakis, “The spectrum of the turbulent near-wake: A comparison of DNS and LES,” 1st AFOSR Int. Conference on DNS/LES, Ruston, LA, 1997 (invited paper).
  64. A. Beskok* and G.E. Karniadakis, “Modeling separation in rarefied gas flows,” AIAA 97-1783, 4th AIAA Shear Flow Conference, Snowmass Village, CO, 1997.
  65. I. Lomtev* and G.E. Karniadakis, “A discontinuous spectral/hp element Galerkin method for the Navier-Stokes equations on unstructured grids,” Proc. IMACS WC’97, Berlin, Germany, 1997.
  66. I. Lomtev* and G.E. Karniadakis, “Simulations of viscous supersonic flows on unstructured h-p meshes,” AIAA 97- 0754, 35th Aerospace Sciences Meeting, Reno, 1997.
  67. X. Ma* and G.E. Karniadakis, “Three-dimensional modeling of unsteady heat transfer,” FEDSM97- 3658, ASME Fluids Engineering Division Summer Meeting, Vancouver, 1997.
  68. T.C. Warburton* and G.E. Karniadakis, “Spectral simulations of flow past a cylinder close to a free surface,” FEDSM973689, ASME Fluids Engineering Division Summer Meeting, Vancouver, 1997.
  69. C. Evangelinos* and G.E. Karniadakis, “Transition in the wake of flexible cables and beams,” 7th ISOPE Conference, Honolulu, Hawaii, 1997.
  70. S.J. Sherwin, C. Evangelinos*, H. Tufo and G.E. Karniadakis, “Development of a parallel unstructured spectral/hp method for unsteady fluid dynamics,” Proc. Parallel CFD’97, May 1997.
  71. D.J. Newman* and G.E. Karniadakis, “Low-dimensional modeling of flow-induced vibrations via proper orthogonal decomposition,” 21st Symposium on Naval Hydrodynamics, Norway, 1996.
  72. C.H. Crawford* and G.E. Karniadakis, “Reynolds stress analysis of controlled wall-bounded turbulence,” AIAA 96- 2008, 27th AIAA Fluid Dynamics Conference, June 17-20, 1996, New Orleans, LA (invited presentation).
  73. C. Evangelinos* and G.E. Karniadakis, “Communication patterns and models in PRISM: A spectral element- Fourier parallel Navier-Stokes solver,” Proc. Supercomputing’96, Pittsburgh, Nov. 17-22, 1996 (finalist for best student paper).
  74. D.J. Newman* and G.E. Karniadakis, “ Direct numerical simulations of flow over a flexible cable,” Sixth Int. Conf. on Flow-Induced Vibrations, Imperial College, April 10-12, 1995, editor P.W. Bearman, Balkema.
  75. D.J. Newman* and G.E. Karniadakis, “Simulations and models of flow over a flexible cable: Standing wave patterns,” ASME/JSME Fluids Engineering Conference, August 1995, Hilton Head SC.
  76. D.J. Newman* and G.E. Karniadakis, “Simulations of flow over a flexible cable: Responses and flow patterns,” AIAA 95-1744, 12th AIAA CFD Conference, June 19-22, 1995, San Diego, CA.
  77. C.H. Crawford* and G.E. Karniadakis, “Control of unsteady flows via electro-magnetic fields,” AIAA 95-2185, 26th AIAA Fluid Dynamics Conference, June 19-22, 1995, San Diego, CA.
  78. A. Beskok*, W. Trimmer, and G.E. Karniadakis, “Rarefaction, compressibility and thermal creep effects for gas microflows,” ASME Annual Winter Meeting, November 1995, San Francisco, CA.
  79. S.J. Sherwin* and G.E. Karniadakis, “Triangular and tetrahedral spectral elements,” ICOSA- HOM’95, June 5-9, 1995, Houston, TX.
  80. T.C. Warburton, S.J. Sherwin and G.E. Karniadakis, “Unstructured hp/spectral elements: Connectivity and optimal ordering,” Int. Conf. on Comp. Engin. Science, July 30-August 3, 1995, Mauna Lani, Hawaii.
  81. T.C. Warburton, S.J. Sherwin and G.E. Karniadakis, “Hierarchical refinement using spectral/hp triangles and prisms,” Sixth Int. Symp. on CFD, September 4-8, 1995, Lake Taho, Nevada.
  82. S.J. Sherwin* and G.E. Karniadakis, “Adaptive hp finite elements on unstructured meshes,” IX Int. Conf. on Finite Elements in Fluids: New Trends and Applications, October 15-21, 1995, Venice, Italy.
  83. S.J. Sherwin* and G.E. Karniadakis, “Tetrahedral spectral elements for CFD,” Proc. 14th Int. Conf. Num. Meth. Fluid Dynamics, July 11-15, 1994, Bangalore, India.
  84. S.J. Sherwin* and G.E. Karniadakis, “A triangular spectral element method: Algorithms and flow applications,” Computational Fluid Dynamics ’94, p. 62, John Wiley Sons, 1994.
  85. R.D. Henderson, C.H. Crawford G.E. Karniadakis, “Structure and statistics of turbulent flow over riblets,” AIAA93-0548, 31st Aerospace Meeting, Reno, 1993.
  86. A.G. Tomboulides*, S.A. Orszag G.E. Karniadakis, “Direct and large eddy simulation of axisymmetric wakes,” AIAA-93-0546, 31st Aerospace Meeting, Reno, 1993.
  87. P.F. Batcho* G.E. Karniadakis, “Global spectral methods for the solution of incompressible Navier- Stokes equations in complex geometries,” Proc. 5th Int. Symp. on CFD, Sendai, Japan, 1993.
  88. J. Trujillo* G.E. Karniadakis, “A spectral element velocity-vorticity algorithm for the incompressible Navier- Stokes equations,” Proc. 5th Int. Symp. on CFD, Sendai Japan, 1993.
  89. R.D. Henderson* and G.E. Karniadakis, “Unstructured spectral element methods for the incompressible Navier- Stokes equations,” in Proc. Finite Elements in Fluids: New Trends and Applications,” eds. K.Morgan, E. Onate, J. Periaux, J. Peraire and O.C. Zienkewicz, Pineridge Press, 1993.
  90. A. Beskok* and G.E. Karniadakis, “Simulation of heat and momentum transfer in complex microgeometries,” AIAA 93-3269, 1st Shear Flow Conference, Orlando, 1993.
  91. H.M. Blackburn and G.E. Karniadakis, “Two-and three-dimensional simulations of vortex-induced vibration of a circular cylinder,” Proc. 3rd ISOPE-93 Conf., vol. 3, p. 715, Singapore, 1993.
  92. J. Giannakouros*, D. Sidilkover G.E. Karniadakis, “Hybrid spectral element methods for hyperbolic systems of conservation laws,” Proc. Fourth Int. Conf. on Hyperb. Problems, Taormina, Italy, April 1992.
  93. S.J. Sherwin*, E. Barough, S.A. Orszag G.E. Karniadakis, “Application of an ENO scheme to simulate the ion etching process,” Proc. Fourth Int. Conf. on Hyperb. Problems, Taormina, Italy, April 1992.
  94. C.H. Crawford, D. Chu G.E. Karniadakis, “Laminar and turbulent flow over optimal riblets,” Proc. First European Conference on CFD, Brussels, 1992, vol. 1, p. 191, ed. C. Hirsch, J. Perriaux W. Kordulla, Elsevier.
  95. M.V. Zagarola, A.J. Smits G.E. Karniadakis, “Heat transfer enhancement in transitional channel flow,” Proc. Second Int. Coll. on Bluff Body Aerodynamics and Applications, Melbourne, 1992.
  96. A. Beskok* G.E. Karniadakis, “Simulation of slip flows in complex microgeometries,” Proc. ASME, Winter Annual Meeting, Anaheim, CA, 1992.
  97. G.E. Karniadakis, S.A. Orszag V. Yakhot, “RNG simulations of transitional and turbulent flow over a backward-facing step,” (invited), Proc. on Large-Eddy Simulation: Where Do We Stand?, St. Petersburg, FL, 1991, also in Large Eddy Simulation of Complex Engineering and Geophysical Flows, p. 159, eds. B. Galperin S.A. Orszag, Cambridge University Press, 1993.
  98. D. Chu* G.E. Karniadakis, “Numerical investigation of drag reduction in flow over surfaces with streamwise aligned riblets,” AIAA-91-0518, 29th Aerospace Sciences Meeting, Reno, 1991.
  99. A.G. Tomboulides*, S.A. Orszag G.E. Karniadakis, “Three-dimensional simulation of flow past a sphere,” Proc. 1st ISOPE-91 Conf., Edinburgh, 1991.
  100. R.D. Henderson* G.E. Karniadakis, “Hybrid spectral element methods for flows over rough walls,” Proc. 5th Conf. on Domain Decomposition Methods, SIAM, 1991.
  101. D. Sidilkover, J. Giannakouros* G.E. Karniadakis, “Hybrid spectral element methods for hyperbolic conservation laws,” Proc. Ninth GAMM Conf. on Num. Meth. in Fluid Mech., Vieweg Verlag, 1991.
  102. D. Chu, R.D. Henderson, G.E. Karniadakis, “Parallel hybrid spectral element methods for incompressible flows,” Proc. 4th Int. Conf. on CFD, Davis, 1991.
  103. G.S. Triantafyllou G.E. Karniadakis, “The route to chaos in the wake of bluff object,” in Research Trends in Physics: Chaotic Dynamics and Transport in Fluids and Plasmas, Ed. I. Prigogine et al., AIP, 1991.
  104. G.S. Triantafyllou G.E. Karniadakis, “The route to turbulence in nominally two-dimensional free shear flows,” Proc. 8th Symp. on Turb. Shear Flows, Munich, 1991.
  105. D. Pathria G.E. Karniadakis, “Dynamic generation of spectral element meshes through wavelet analysis,” USA-French Workshop on Wavelets and Turbulence, Princeton, 1991, (unpublished).
  106. G.E. Karniadakis, “Three-dimensional equilibria and transition in complex geometry flows,” Proc. 1st IMACS Int. Conf. on Comp. Phys., 1990, (invited).
  107. G.E. Karniadakis G.S. Triantafyllou, “Direct numerical simulation of the three-dimensional vortex street,” AIAA90-0113, 28th Aerospace Sciences Meeting, Reno, 1990.
  108. A.G. Tomboulides*, S.A. Orszag G.E. Karniadakis, “Three-dimensional simulation of flow past a sphere,” U.S. Nat’l Congress on Theor. Appl. Mech., Tucson, AZ, 1990, (invited).
  109. G.E. Karniadakis S.A. Orszag, “Spectral simulations of complex flows,” Proc. 5th Int. Conf. on Sciences and Engineering on Supercomputers, London, 1990, (invited).
  110. E. Barough, B. Bradie, U. Hollerbach, G.E. Karniadakis S.A. Orszag, “Comprehensive 3-D notching simulator with non-planar substrates,” Proc. on Optical/Laser Microlithography, vol. 3, p. 334, SPIE, 1990.
  111. G.E. Karniadakis, A. Yakhot , S.A. Orszag V. Yakhot, “Spectral element-RNG simulations of turbulent heat transfer in complex geometries,” Proc. 9th Int. Heat Transfer Conf., vol. 3, p. 247, 1990.
  112. G.E. Karniadakis, S.A. Orszag V. Yakhot, “Large eddy/RNG simulation of flow over a backward-facing step,” in Engineering Turbulence: Modeling and Experiments, Elsevier, p. 269, 1990.
  113. C. Berman, J. Ramos, G.E. Karniadakis S.A. Orszag, “Time-dependent jet flow and noise computations,” AIAA-903961, 13th Aero-acoustics Conf., Tallahassee, 1990.
  114. G.E. Karniadakis, A. Yakhot, S. Rakib, S. Orszag V. Yakhot, “Spectral element-RNG simulation of turbulent flows in complex geometries,” Proc. 7th Symp. on Turb. Shear Flows, Stanford, 1989.
  115. C. Mavriplis, P. Fischer G.E. Karniadakis. “Direct numerical simulation of the impulsive flow past a wedge-like corner,” Proc. 10th Austr. Fluid Mech. Conf., vol. II, 1989.
  116. G.S. Triantafyllou G.E. Karniadakis, “Forces on a vibrating cylinder in steady cross-flow,” Proc. 8th OMAE (Offshore Mech Arctic Eng.) Conf., Hague, 1989.
  117. C. Begue, C. Bernardi, N. Debit, Y. Maday, G.E. Karniadakis A.T. Patera, “Nonconforming spectral element-finite element approximations for the Navier-Stokes equations,” Proc. 8th Int. Conf. on Comp. Methods in Applied Science and Engineering, Versaille, 1987, also in C.M.A.M.E., vol. 75, p. 109, 1989.
  118. G.E. Karniadakis, S.A. Orszag, A. Yakhot and V. Yakhot, “RNG modeling techniques for complex turbulent flows,” Proc. 5th Int. Conf. on Num. Ship Hydrodynamics, Hiroshima, 1989, (invited).
  119. Y. Maday, A.T. Patera G.E. Karniadakis, “Spectral and finite element approximation for the unsteady incompressible Euler equations,” Notes aux Reudus de l’Academie des Sciences, Paris, 1987, (invited).
  120. G.E. Karniadakis C. Amon, “Stability calculations of wall bounded flows in complex geometries,” Proc. 6th IMACS Symp. on P.D.E.s, p. 525, 1987, (invited).
  121. G.E. Karniadakis, B.B. Mikic A.T. Patera, “Heat transfer enhancement by flow destabilization: Application to the cooling of chips,” Int. Symp. on Cooling Technology for Electronic Equipment, Hemisphere, p. 587, 1987.
  122. M. Greiner, G.E. Karniadakis, B.B. Mikic A.T. Patera, “Heat transfer augmentation and hydro-dynamic stability theory: Understanding and exploitation,” Proc. Heat Transfer Conf., Korea, 1986.
  123. E.T. Bullister, G.E. Karniadakis, E.M. Ronquist A.T. Patera, “Solutions of the unsteady Navier- Stokes equations by spectral element methods,” Proc. 6th Int. Symp. on Finite Element Methods in Flow Problems, Antibes, 1986.
  124. G.E. Karniadakis, B.B. Mikic A.T. Patera, “Unsteady heat transfer from a cylinder in crossflow: A direct numerical simulation,” Proc. 8th Int. Heat Transfer Conf., vol. 2, p. 429, 1986.
  125. G.E. Karniadakis, E.T. Bullister, B.B. Mikic A.T. Patera, “A spectral element method applied to the cooling of electronic components,” Proc. AIAA/ASME Thermod. and Heat Transfer Conf., Boston, 1986.
  126. G.E. Karniadakis A.T. Patera, “A spectral element method for the simulation of unsteady incompressible flows with heat transfer,” Proc. 4th Int. Symp. on Num. Meth. in Eng., Springer, p. 231, 1986.
  127. G.E. Karniadakis, E.T. Bullister A.T. Patera, “A spectral element method for solution of two-and three- dimensional time-dependent incompressible Navier-Stokes equations,” Proc. Europe-U.S. Conf. on Finite Element Methods for Nonlinear Problems, Springer-Verlag, p. 803, 1985.