78 citations · 426 across the 35 of their papers we have counts for
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Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations
Yuan Liu, Yingda Cheng, Shanqin Chen +1
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to la…
Dispersion Analysis of Finite Difference and Discontinuous Galerkin Schemes for Maxwell's Equations in Linear Lorentz Media
Yan Jiang, Puttha Sakkaplangkul, Vrushali A. Bokil +2
In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly use…
Sparse Grid Central Discontinuous Galerkin Method for Linear Hyperbolic Systems in High Dimensions
Zhanjing Tao, Anqi Chen, Mengping Zhang +1
In this paper, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines t…
Sparse Grid Discontinuous Galerkin Methods for the Vlasov-Maxwell System
Zhanjing Tao, Wei Guo, Yingda Cheng
In this paper, we develop sparse grid discontinuous Galerkin (DG) schemes for the Vlasov-Maxwell (VM) equations. The VM system is a fundamental kinetic model in plasma physics, and…
An Ultra-Weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension
Anqi Chen, Fengyan Li, Yingda Cheng
In this paper, we develop an ultra-weak discontinuous Galerkin (DG) method to solve the one-dimensional nonlinear Schrödinger equation. Stability conditions and error estimates are…