On the scalability of the Schwarz method

DOI10.5802/smai-jcm.61zbMath1447.65175arXiv1902.03670OpenAlexW3018278225MaRDI QIDQ2188102

Gabriele Ciaramella, Muhammad Hassan, Benjamin Stamm

Publication date: 3 June 2020

Published in: SMAI Journal of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.03670

zbMATH Keywords

Schwarz methodsdomain decomposition methodsLaplace equationscalability analysischain of atomsddCOSMO

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Boundary value problems for second-order elliptic systems (35J57)

Related Items (5)

Spectral coarse spaces for the substructured parallel Schwarz method ⋮ Linear and nonlinear substructured restricted additive Schwarz iterations and preconditioning ⋮ Substructured two-grid and multi-grid domain decomposition methods ⋮ Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices ⋮ Analysis of the Schwarz Domain Decomposition Method for the Conductor-like Screening Continuum Model

Uses Software

• Anderson

Cites Work

• Schwarz methods over the course of time
• On the scalability of classical one-level domain-decomposition methods
• Overlapping Schwarz waveform relaxation for the heat equation in \(n\) dimensions
• Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. III.
• An integral equation approach to calculate electrostatic interactions in many-body dielectric systems
• Anderson Acceleration for Fixed-Point Iterations
• Uniform Convergence of the Schwarz Alternating Method for Solving Singularly Perturbed Advection-Diffusion Equations
• Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II
• A domain decomposition method for the polarizable continuum model based on the solvent excluded surface
• Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-Sized Subdomains: Part I
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