43 citations · 118 across the 13 of their papers we have counts for
14 papers
Well-balanced path-conservative discontinuous Galerkin methods with equilibrium preserving space for shallow water linearized moment equations
Ruilin Fan, Julian Koellermeier, Yinhua Xia +2
This paper presents high-order, well-balanced, path-conservative discontinuous Galerkin (DG) methods for the shallow water linearized moment equations (SWLME), designed to preserve…
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…
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…
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…
Discontinuous Galerkin method based on the reduced space for the nonlinear convection-diffusion-reaction equation
Shijin Hou, Yinhua Xia
In this paper, by introducing a reconstruction operator based on the Legendre moments, we construct a reduced discontinuous Galerkin (RDG) space that could achieve the same approxi…
Structure-preserving finite volume arbitrary Lagrangian-Eulerian WENO schemes for the shallow water equations
Jiahui Zhang, Yinhua Xia, Yan Xu
This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary Lagrangian…
Fast optimal mass transport via reduced basis methods for the Monge-Ampre equation
Shijin Hou, Yanlai Chen, Yinhua Xia
Repeatedly solving the parameterized optimal mass transport (pOMT) problem is a frequent task in applications such as image registration and adaptive grid generation. It is thus cr…
A well-balanced oscillation-free discontinuous Galerkin method for shallow water equations
Yong Liu, Jianfang Lu, Qi Tao +1
In this paper, we develop a well-balanced oscillation-free discontinuous Galerkin (OFDG) method for solving the shallow water equations with a non-flat bottom topography. One notab…
Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation
Qian Zhang, Yinhua Xia
In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as pe…
Discontinuous Galerkin methods for short pulse type equations via hodograph transformations
Qian Zhang, Yinhua Xia
In the present paper, we consider the discontinuous Galerkin (DG) methods for solving short pulse (SP) type equations. The short pulse equation has been shown to be completely inte…
Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws on moving simplex meshes
Pei Fu, Gero Schnücke, Yinhua Xia
In Klingenberg, Schnücke and Xia (Math. Comp. 86 (2017), 1203-1232) an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method to solve conservation laws has been deve…
Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations
J. J. W. van der Vegt, Yinhua Xia, Yan Xu
Currently, nearly all positivity preserving discontinuous Galerkin (DG) discretizations of partial differential equations are coupled with explicit time integration methods. Unfort…
Binary black hole simulation with an adaptive finite element method II: Application of local discontinuous Galerkin method to Einstein equations
Zhoujian Cao, Pei Fu, Li-Wei Ji +1
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve p…
Turbulence in the Inter-galactic Medium: Solenoidal and Dilatational Motions, and the Impact of Numerical Viscosity
Weishan Zhu, Long-Long Feng, Yinhua Xia +3
We use a suite of cosmological hydrodynamic simulations, run by two fixed grid codes, to investigate the properties of solenoidal and dilatational motions of the intergalactic medi…