31 citations · 63 across the 16 of their papers we have counts for
16 papers
On a Sharp Estimate of Overlapping Schwarz Methods in and
Qigang Liang, Xuejun Xu, Shangyou Zhang
The previous proved-bound is for the condition number of the overlapping domain decomposition and …
Domain Decomposition Methods for Elliptic Problems with High Contrast Coefficients Revisited
Xuyang Na, Xuejun Xu
In this paper, we revisit the nonoverlapping domain decomposition methods for solving elliptic problems with high contrast coefficients. Some interesting results are discovered. We…
Domain Decomposition Learning Methods for Solving Elliptic Problems
Qi Sun, Xuejun Xu, Haotian Yi
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods,…
A Two-Level Block Preconditioned Jacobi-Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators
Qigang Liang, Wei Wang, Xuejun Xu
In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approxim…
A Two-Level Preconditioned Helmholtz-Jacobi-Davidson Method for the Maxwell Eigenvalue Problem
Qigang Liang, Xuejun Xu
In this paper, based on a domain decomposition (DD) method, we shall propose an efficient two-level preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for solving the algebraic…
Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations
Tingting Hao, Manman Ma, Xuejun Xu
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singulariti…
Regularity results for the time-harmonic Maxwell equations with impedance boundary condition
Peipei Lu, Yun Wang, Xuejun Xu
This paper considers the time-harmonic Maxwell equations with impedance boundary condition.We present -norm bound and other high-order norm bounds for strong solutions. The $H…
A Monotone Finite Volume Method for Time Fractional Fokker-Planck Equations
Yingjun Jiang, Xuejun Xu
We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of…
Domain Decomposition Methods for Space Fractional Partial Differential Equations
Yingjun Jiang, Xuejun Xu
In this paper, a two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partia…
Multigrid Methods for Space Fractional Partial Differential Equations
Yingjun Jiang, Xuejun Xu
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is…
A FETI-DP preconditioner of discontinuous Galerkin method for multiscale problems in high constrast media
Rui Du, Yunfei Ma, Talal Rahman +1
In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discre…
A Robust Multilevel Method for Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation
Huangxin Chen, Peipei Lu, Xuejun Xu
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are tw…
Multilevel Preconditioner with Stable Coarse Grid Corrections for the Helmholtz Equation
Huangxin Chen, Haijun Wu, Xuejun Xu
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior p…
A Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation with High Wave Number
Huangxin Chen, Peipei Lu, Xuejun Xu
This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The ap…
Domain Decomposition Preconditioners for a Discontinuous Galerkin Formulation of a Multiscale Elliptic Problem
Yunfei Ma, Petter Bjorstad, Talal Rahman +1
In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on…
On the optimal convergence rate of a Robin-Robin domain decomposition method
Wenbin Chen, Xuejun Xu, Shangyou Zhang
In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition(DD) method can be constant,…