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Fast Maxwell Solvers Based on Exact Discrete Eigen-Decompositions I. Two-Dimensional Case
Lixiu Wang, Lueling Jia, Zijian Cao +2
In this paper, we propose fast solvers for Maxwell's equations in rectangular domains. We first discretize the simplified Maxwell's eigenvalue problems by employing the lowest-orde…
Sparse Spectral-Galerkin Method on An Arbitrary Tetrahedron Using Generalized Koornwinder Polynomials
Lueling Jia, Huiyuan Li, Zhimin Zhang
In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koorn…
A -conforming Petrov-Galerkin method for convection-diffusion equations and superconvergence ananlysis over rectangular meshes
Waixiang Cao, Lueling Jia, Zhimin Zhang
In this paper, a new -conforming Petrov-Galerkin method for convection-diffusion equations is designed and analyzed. The trail space of the proposed method is a -conformi…
A Petrov-Galerkin method and Gauss collocation method for 1D general elliptic problems and superconvergence
Waixiang Cao, Lueling Jia, Zhimin Zhang
In this paper, we present and study Petrov-Galerkin and Gauss collocation methods with arbitrary polynomial degree () for one-dimensional elliptic equations. We pr…
Generalised Hermite spectral methods for PDEs involving integral fractional Laplacian and Schrödinger operators
Changtao Sheng, Suna Ma, Huiyuan Li +2
In this paper, we introduce two new families of generalised Hermite polynomials/functions (GHPs/GHFs) in arbitrary dimensions, and develop efficient and accurate generalised Hermit…