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- research-articleAugust 2024
A global space–time Trefftz DG scheme for the time-dependent isotropic elastic wave equations
Journal of Computational and Applied Mathematics (JCAM), Volume 450, Issue Chttps://doi.org/10.1016/j.cam.2024.115931AbstractIn this paper we are concerned with Trefftz discretizations of the time-dependent linear elastic wave equation in arbitrary space dimensional domains Ω ⊂ R d ( d ∈ N ). We propose a Trefftz discontinuous Galerkin method, construct Trefftz basis ...
- research-articleJuly 2024
- research-articleJuly 2024
A Parallel Finite Element Discretization Scheme for the Natural Convection Equations
Journal of Scientific Computing (JSCI), Volume 100, Issue 2https://doi.org/10.1007/s10915-024-02601-6AbstractThis article presents a parallel finite element discretization scheme for solving numerically the steady natural convection equations, where a fully overlapping domain decomposition technique is used for parallelization. In this scheme, each ...
- research-articleJune 2024
A Multiscale Finite Element Method for an Elliptic Distributed Optimal Control Problem with Rough Coefficients and Control Constraints
Journal of Scientific Computing (JSCI), Volume 100, Issue 2https://doi.org/10.1007/s10915-024-02590-6AbstractWe construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale ...
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- research-articleApril 2024
A family of Nonoverlapping Spectral Additive Schwarz methods (NOSAS) and their economic versions
Journal of Computational and Applied Mathematics (JCAM), Volume 443, Issue Chttps://doi.org/10.1016/j.cam.2023.115734AbstractNOSAS (Nonoverlapping Spectral Additive Schwarz) methods are nonoverlapping iterative domain decomposition methods for efficiently solving large sparse linear systems arising from elliptic problems with heterogeneous coefficients. NOSAS methods ...
- research-articleMarch 2024
Non-overlapping domain decomposition algorithms with only primal velocity unknowns for the discontinuous viscosity Stokes problem
Journal of Computational and Applied Mathematics (JCAM), Volume 440, Issue Chttps://doi.org/10.1016/j.cam.2023.115640AbstractIn this paper, non-overlapping domain decomposition algorithms for the Stokes problem with a discontinuous viscosity coefficient are proposed and analyzed. A pair of inf–sup stable finite element spaces with discontinuous pressure finite element ...
- research-articleFebruary 2024
Modeling Excitable Cells with the EMI Equations: Spectral Analysis and Iterative Solution Strategy
Journal of Scientific Computing (JSCI), Volume 98, Issue 3https://doi.org/10.1007/s10915-023-02449-2AbstractIn this work, we are interested in solving large linear systems stemming from the extra–membrane–intra model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial differential ...
- research-articleJanuary 2024
An Aggregation-Based Two-Grid Method for Multilevel Block Toeplitz Linear Systems
Journal of Scientific Computing (JSCI), Volume 98, Issue 3https://doi.org/10.1007/s10915-023-02434-9AbstractThis paper presents an aggregation-based two-grid method for solving a multilevel block Toeplitz system. Different from the existing multigrid methods for multilevel block Toeplitz systems, we aggregate a given multilevel block Toeplitz matrix to ...
- research-articleDecember 2023
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions
Advances in Computational Mathematics (SPACM), Volume 50, Issue 1https://doi.org/10.1007/s10444-023-10101-8AbstractBased on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible Navier-Stokes equations, where non-...
- review-articleJuly 2023
A Unified Theory of Non-overlapping Robin–Schwarz Methods: Continuous and Discrete, Including Cross Points
Journal of Scientific Computing (JSCI), Volume 96, Issue 2https://doi.org/10.1007/s10915-023-02248-9AbstractNon-overlapping Schwarz methods with generalized Robin transmission conditions were originally introduced by B. Després for time-harmonic wave propagation problems and have largely developed over the past thirty years. The aim of the paper is to ...
- research-articleMay 2023
Multilevel Uzawa and Arrow–Hurwicz Algorithms for General Saddle Point Problems
Journal of Optimization Theory and Applications (JOPT), Volume 198, Issue 2Pages 678–709https://doi.org/10.1007/s10957-023-02231-2AbstractIn this paper, we introduce and analyze multilevel inexact Uzawa and Arrow–Hurwicz algorithms for solving saddle point problems. For the definition of the problem and that of the Uzawa and Arrow–Hurwicz algorithms, we adopt the framework ...
- research-articleMay 2023
A Semi Matrix-Free Twogrid Preconditioner for the Helmholtz Equation with Near Optimal Shifts
Journal of Scientific Computing (JSCI), Volume 95, Issue 3https://doi.org/10.1007/s10915-023-02195-5AbstractDue to its significance in terms of wave phenomena a considerable effort has been put into the design of preconditioners for the Helmholtz equation. One option to design a preconditioner is to apply a multigrid method on a shifted operator. In ...
- research-articleApril 2023
Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex
Foundations of Computational Mathematics (FOCM), Volume 24, Issue 3Pages 1019–1048https://doi.org/10.1007/s10208-023-09611-0AbstractThis work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning (Hiptmair and Xu in SIAM J Numer Anal 45:2483–2509, 2007). In particular, on unstructured ...
- research-articleMarch 2023
A parallel two-grid method based on finite element approximations for the 2D/3D Navier–Stokes equations with damping
Engineering with Computers (ENGC), Volume 40, Issue 1Pages 541–554https://doi.org/10.1007/s00366-023-01807-wAbstractBased on two-grid discretizations, this paper introduces a parallel finite element method for the 2D/3D Navier–Stokes equations with damping. In this method, we first solve a fully nonlinear problem on a global coarse grid, and then solve ...
- research-articleMarch 2023
Numerical solutions of Gelfand equation in steady combustion process
Applied Mathematics and Computation (APMC), Volume 441, Issue Chttps://doi.org/10.1016/j.amc.2022.127674Highlights- We consider the application of cascadic multigrid method for finding all solutions of Gelfand equation.
In this paper, we study a numerical algorithm to find all solutions of Gelfand equation. By utilizing finite difference discretization, the model problem defined on bounded domain with Dirichlet condition is converted to a nonlinear ...
- research-articleMarch 2023
Novel mass-based multigrid relaxation schemes for the Stokes equations
Applied Mathematics and Computation (APMC), Volume 440, Issue Chttps://doi.org/10.1016/j.amc.2022.127665AbstractIn this work, we propose three novel block-structured multigrid relaxation schemes based on distributive relaxation, Braess–Sarazin relaxation, and Uzawa relaxation, for solving the Stokes equations discretized by the marker-and-cell scheme. The ...