Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II

DOI10.1137/17M1115885zbMath1435.65223OpenAlexW4231207954MaRDI QIDQ4564034

Martin J. Gander, Gabriele Ciaramella

Publication date: 12 June 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1115885

zbMATH Keywords

Schwarz methodsdomain decomposition methodsLaplace equationelliptic PDEchain of atomsCOSMO solvation 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 (13)

On the scalability of classical one-level domain-decomposition methods ⋮ 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 ⋮ On the scalability of the Schwarz method ⋮ A Coarse Space to Remove the Logarithmic Dependency in Neumann–Neumann Methods ⋮ Multilevel Optimized Schwarz Methods ⋮ A Domain Decomposition Method for the Poisson--Boltzmann Solvation Models ⋮ Analysis of the parallel Schwarz method for growing chains of fixed-sized subdomains. III. ⋮ Optimized Schwarz methods with elliptical domain decompositions ⋮ Methods of reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning. ⋮ 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

Cites Work

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• Block Jacobi for Discontinuous Galerkin Discretizations: No Ordinary Schwarz Methods
• On the Influence of Curvature on Transmission Conditions
• Block Jacobi Relaxation for Plane Wave Discontinuous Galerkin Methods
• Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: The many-subdomain case
• Analysis of Schwarz Methods for a Hybridizable Discontinuous Galerkin Discretization
• Continuous analysis of the additive Schwarz method: A stable decomposition inH¹with explicit constants
• Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-Sized Subdomains: Part I
• Optimized Schwarz Methods
• Introduction to Partial Differential Equations

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