Optimal Interface Conditions for an Arbitrary Decomposition into Subdomains

DOI10.1007/978-3-642-11304-8_9zbMath1217.65223OpenAlexW2198737122MaRDI QIDQ2998409

Martin J. Gander, Felix Kwok

Publication date: 18 May 2011

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-11304-8_9

zbMATH Keywords

convergencenumerical examplesdomain decompositionDirichlet-to-Neumann operatorstransmission conditionsoptimal Schwarz methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Related Items (14)

An introduction to multi-trace formulations and associated domain decomposition solvers ⋮ L-sweeps: a scalable, parallel preconditioner for the high-frequency Helmholtz equation ⋮ On the Definition of Dirichlet and Neumann Conditions for the Biharmonic Equation and Its Impact on Associated Schwarz Methods ⋮ SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation ⋮ Schwarz methods by domain truncation ⋮ Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation ⋮ Cross-points in the Dirichlet-Neumann method. I: Well-posedness and convergence issues ⋮ On Optimal Coarse Spaces for Domain Decomposition and Their Approximation ⋮ An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation ⋮ A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods ⋮ A Continuous Analysis of Neumann--Neumann Methods: Scalability and New Coarse Spaces ⋮ A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation ⋮ The method of polarized traces for the 2D Helmholtz equation ⋮ On the Relation Between Optimized Schwarz Methods and Source Transfer

Cites Work

• Unnamed Item
• Why restricted additive Schwarz converges faster than additive Schwarz
• Optimal Discrete Transmission Conditions for a Nonoverlapping Domain Decomposition Method for the Helmholtz Equation
• FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM
• Optimized Schwarz Methods without Overlap for the Helmholtz Equation
• Optimized Schwarz Methods

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