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math.NA2025★ 1 cited
Kernel compensation method for Maxwell eigenproblem with mimetic finite difference discretization
Chenhao Jin, Yinhua Xia, Yan Xu
We present a kernel compensation method for Maxwell eigenproblem for photonic crystals to avoid the infinite-dimensional kernels that cause many difficulties in the calculation of…
math.NA2024
Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for two-layer shallow water equations
Jiahui Zhang, Yinhua Xia, Yan Xu
This paper introduces well-balanced path-conservative discontinuous Galerkin (DG) methods for two-layer shallow water equations, ensuring exactness for both still water and moving…
math.NA2024★ 1 cited
Equilibrium preserving space in discontinuous Galerkin methods for hyperbolic balance laws
Jiahui Zhang, Yinhua Xia, Yan Xu
In this paper, we develop a general framework for the design of the arbitrary high-order well-balanced discontinuous Galerkin (DG) method for hyperbolic balance laws, including the…