Multilevel Optimized Schwarz Methods

DOI10.1137/19M1259389zbMath1475.65212OpenAlexW3093424331MaRDI QIDQ5132010

Martin J. Gander, Tommaso Vanzan

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1259389

zbMATH Keywords

optimized Schwarz methodsmultilevel domain decomposition methodsheterogeneous two-level solvertwo-level Helmholtz solvertwo-level Stokes-Darcy solver

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Flows in porous media; filtration; seepage (76S05) 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) Optimality conditions for minimax problems (49K35) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (4)

Spectral coarse spaces for the substructured parallel Schwarz method ⋮ Substructured two-grid and multi-grid domain decomposition methods ⋮ Ensemble Domain Decomposition Algorithm for the Fully Mixed Random Stokes–Darcy Model with the Beavers–Joseph Interface Conditions ⋮ Two-grid domain decomposition methods for the coupled Stokes-Darcy system

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation
• On the scalability of classical one-level domain-decomposition methods
• Optimized Schwarz methods for advection diffusion equations in bounded domains
• A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator
• The Optimized Schwarz Method with a Coarse Grid Correction
• Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
• Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption
• Optimized Schwarz Methods for Maxwell Equations with Discontinuous Coefficients
• Discontinuous Coarse Spaces for DD-Methods with Discontinuous Iterates
• Convergence Behavior of a Two-Level Optimized Schwarz Preconditioner
• An Introduction to Domain Decomposition Methods
• Parallel Multilevel Preconditioners
• Optimized Multiplicative, Additive, and Restricted Additive Schwarz Preconditioning
• Optimized Schwarz Methods for Maxwell's Equations
• An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation
• A Lions non-overlapping domain decomposition method for domains with an arbitrary interface
• Iterative Methods by Space Decomposition and Subspace Correction
• Optimized Schwarz methods for the Stokes–Darcy coupling
• Analysis of the Parallel Schwarz Method for Growing Chains of Fixed-sized Subdomains: Part II
• Optimized Schwarz Methods without Overlap for the Helmholtz Equation
• New development in freefem++
• Two-Level Preconditioners for the Helmholtz Equation
• A Finite Difference Method with Optimized Dispersion Correction for the Helmholtz Equation
• Complete, Optimal and Optimized Coarse Spaces for Additive Schwarz
• Heterogeneous Optimized Schwarz Methods for Coupling Helmholtz and Laplace Equations
• A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections
• Heterogeneous Optimized Schwarz Methods for Second Order Elliptic PDEs
• SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation
• Optimized Schwarz Methods

This page was built for publication: Multilevel Optimized Schwarz Methods