2018
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. M Ainsworth, C Glusa
Hybrid Finite Element–Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver. M Ainsworth, C Glusa
The Resiliency of Multilevel Methods on Next Generation Computing Platforms: Probabilistic Model and Its Analysis. CA Glusa, M Ainsworth
A view from ORNL: Scientific data research opportunities in the big data age. S Klasky, M Wolf, M Ainsworth, C Atkins, J Choi, G Eisenhauer, B Geveci, et al.
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. M Ainsworth, G Fu
Coupling exascale multiphysics applications: Methods and lessons learned. JY Choi, CS Chang, J Dominski, S Klasky, G Merlo, E Suchyta, et al.
Multilevel techniques for compression and reduction of scientific data—the univariate case. M Ainsworth, O Tugluk, B Whitney, S Klasky
Bernstein-Bezier bases for tetrahedral finite elements, Mark Ainsworth and Guosheng Fu.
Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems. Haijin Wang, Qiang Zhang, Chi-Wang Shu.
The L2-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations. Yuan Xu, Qiang Zhang, Chi-Wang Shu, and Haijin Wang.
Well-balanced finite volume schemes for hydrodynamic equations with general free energy. Jose A. Carrillo, Serafim Kalliadasis, Sergio P. Perez, and Chi-Wang Shu.
Strong stability of explicit Runge-Kutta Time Discretizations. Zheng Sun and Chi-Wang Shu.
An entropy stable high-order discontinuous Galerkin method for cross-diffusion in gradient flow systems. Zheng Sun, Jose A. Carrillo and Chi-Wang Shu.
High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. Feng Zheng, Chi-Wang Shu and Jianxian Qiu.
A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows. Jantao Huang, Weifeng Zhao, and Chi-Wang Shu.
Completed Repeated Richarson Extrapolation for compressible fluid flows. Nicholas Dicati Pereira da Silva, Carlos Henrique Marchi, Luciano, Kiyoshi, Rafael Brandao de Rezende Borges, Guilherme Bertoldo, Chi-Wang Shu.
Provably Positive High-Order Schemes for IdealMagnetohydrodynamics: Analysis on General Meshes. Kailiang Wu and Chi-Wang Shu.
A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Jun Zhu and Chi-Wang Shu.
Locally divergence-free spectral-DG methods for idealmagnetohydrodynamic equations on cylindrical coordinates. Yong Liu, Qingyuan Liu, Yuan Liu, Chi-Wang Shu and Mengping Zhang.
Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Young Liu, Chi-Wang Shu and Mengping Zhang.
Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. Juntao Huang and Chi-Wang Shu.
An energy-conserving ultra-weak discontinuous Galerkin Method for the generalized Korteweg-De Vries Equation. Guosheng Fu and Chi-Wang Shu.
Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. Guosheng Fu and Chi-Wang Shu.
Modeling and simulation of urban air pollution from the dispersion of vehicle exhaust: A continuum modeling approach. Liangze Yang, Tingting Li, S.C. Wong, Chi-Wang Shu, Mengping Zhang.
Numerical solutions of stochastic PDEs driven by arbitrary type of noise. Tianheng Chen, Boris Rozovskii and Chi-Wang Shu.
Stability analysis and errorestimates of arbitrary Lagragian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws. Lingling Zhou, Yinhua Xia and Chi Wang Shu.
Provably positive discontinuous Galerkin methods for multidimensional ideal magnetohydrodynamics. Kailiang Wu and Chi-Wang Shu.
Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems. Haijin Wang, Qiang Zhang, Shiping Wang, and Chi-Wang Shu.
Discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials on unstructured meshes. Cengke Shi, Lichun Li and Chi-Wang Shu.
Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations. Dan Ling, Juan Cheng, Chi-Wang Shu.
Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions. Haijin Wang, Qiang Zhang, Chi-Wang Shu.