On the scalability of classical one-level domain-decomposition methods

DOI10.1007/s10013-018-0316-9zbMath1406.65128OpenAlexW2901300391WikidataQ128949501 ScholiaQ128949501MaRDI QIDQ1633795

Faycal Chaouqui, Tommaso Vanzan, Martin J. Gander, Gabriele Ciaramella

Publication date: 20 December 2018

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-018-0316-9

zbMATH Keywords

scalabilityLaplace's equationchain of atomsdomain-decomposition methodsclassical and optimized Schwarz methodsDirichlet-Neumann methodNeumann-Neumann methodsolvation model

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Boundary value problems for second-order elliptic systems (35J57)

Related Items (16)

Spectral coarse spaces for the substructured parallel Schwarz method ⋮ Substructured two-grid and multi-grid domain decomposition methods ⋮ Closed Form Optimized Transmission Conditions for Complex Diffusion with Many Subdomains ⋮ Optimized Schwarz Methods for the Cahn–Hilliard Equation ⋮ On the scalability of the Schwarz method ⋮ Cross-points in the Dirichlet-Neumann method. I: Well-posedness and convergence issues ⋮ Convergence of linear and nonlinear Neumann-Neumann method for the Cahn-Hilliard equation ⋮ Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems ⋮ Convergence of substructuring methods for the Cahn-Hilliard equation ⋮ Multilevel Optimized Schwarz Methods ⋮ A Continuous Analysis of Neumann--Neumann Methods: Scalability and New Coarse Spaces ⋮ Methods of reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning. ⋮ Convergence Analysis of the Nonoverlapping Robin--Robin Method for Nonlinear Elliptic Equations ⋮ Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices ⋮ How to best choose the outer coarse mesh in the domain decomposition method of Bank and Jimack ⋮ Analysis of the Schwarz Domain Decomposition Method for the Conductor-like Screening Continuum Model

Uses Software

• Maple
• Matlab

Cites Work

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• Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems
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