11 citations · 35 across the 19 of their papers we have counts for
19 papers
Error Analysis of Virtual Element Method for the Poisson-Boltzmann Equation
Linghan Huang, Shi Shu, Ying Yang
The Poisson-Boltzmann equation is a nonlinear elliptic equation with Dirac distribution sources, which has been widely applied to the prediction of electrostatics potential of biol…
Fourier Neural Solver for large sparse linear algebraic systems
Chen Cui, Kai Jiang, Yun Liu +1
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In…
An Improved Multi-Stage Preconditioner on GPUs for Compositional Reservoir Simulation
Li Zhao, Chen-Song Zhang, Chun-Sheng Feng +1
The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak c…
Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations
Ying Yang, Ya Liu, Shi Shu
We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely us…
Parallel Multi-Stage Preconditioners with Adaptive Setup for the Black Oil Model
Li Zhao, Chunsheng Feng, Chensong Zhang +1
The black oil model is widely used to describe multiphase porous media flow in the petroleum industry. The fully implicit method features strong stability and weak constraints on t…
Solving time-dependent parametric PDEs by multiclass classification-based reduced order model
Chen Cui, Kai Jiang, Shi Shu
In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (P…
Two-level overlapping Schwarz methods based on local generalized eigenproblems for Hermitian variational problems
Qing Lu, Junxian Wang, Shi Shu +1
The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly…
Algebraic multigrid block preconditioning for multi-group radiation diffusion equations
Xiaoqiang Yue, Shulei Zhang, Xiaowen Xu +2
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully…
Local Averaging Type a Posteriori Error Estimates for the Nonlinear Steady-state Poisson-Nernst-Planck Equations
Ying Yang, Ruigang Shen, Mingjuan Fang +1
The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst-Planck equations, which are a coupled system consisting of the Nernst-Planck equati…
Adaptive-Multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems
Jie Peng, Shi Shu, Junxian Wang +1
In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algori…
A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems
Xiaoqiang Yue, Kejia Pan, Jie Zhou +3
The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to…
Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations
Xiaoqiang Yue, Shi Shu, Xiaowen Xu +2
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discre…
A Decoupling Two-grid Method for the Time-dependent Poisson-Nernst-Planck Equations
Ruigang Shen, Shi Shu, Ying Yang +1
We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The comput…
Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations
Jie Peng, Junxian Wang, Shi Shu
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-…
Time-space Finite Element Adaptive AMG for Multi-term Time Fractional Advection Diffusion Equations
Xiaoqiang Yue, Yehong Xu, Shi Shu +2
In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equa…
Fully Finite Element Adaptive Algebraic Multigrid Method for Time-Space Caputo-Riesz Fractional Diffusion Equations
Xiaoqiang Yue, Weiping Bu, Shi Shu +2
The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equati…
An adaptive BDDC algorithm in variational form for mortar discretizations
Jie Peng, Shi Shu, Junxian Wang
A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretizatio…
Error estimates on a finite volume method for diffusion problems with interface on Eulerian grids
Jie Peng, Shi Shu, Haiyuan Yu +3
The finite volume methods are frequently employed in the discretization of diffusion problems with interface. In this paper, we firstly present a vertex-centered MACH-like finite v…
Numerical Study of Geometric Multigrid Methods on CPU--GPU Heterogeneous Computers
Chunsheng Feng, Shi Shu, Jinchao Xu +1
The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utiliz…