Balancing domain decomposition for problems with large jumps in coefficients

DOI10.1090/S0025-5718-96-00757-0zbMath0853.65129MaRDI QIDQ4718394

Jan Mandel, Marian Brezina

Publication date: 3 December 1996

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

zbMATH Keywords

discontinuous coefficientsdomain decompositionsecond-order elliptic boundary value problemstwo-level iterative methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Iterative numerical methods for linear systems (65F10)

Related Items

Optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients, Extended preconditioners for the FETI method applied to constrained problems, Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems, Balancing Neumann-Neumann methods for incompressible Stokes equations, Scalable preconditioning for the stabilized contact mechanics problem, Avoiding singular coarse grid systems, An iterative solver for \(p\)-version finite elements in three dimensions, Fully implicit local time-stepping methods for advection-diffusion problems in mixed formulations, Neumann-Neumann methods for a DG discretization on geometrically nonconforming substructures, Positive definite balancing Neumann-Neumann preconditioners for nearly incompressible elasticity, An asymptotic solution approach for elliptic equations with discontinuous coefficients, Linear and nonlinear substructured restricted additive Schwarz iterations and preconditioning, Neumann-Neumann-Schur complement methods for Fekete spectral elements, FETI and Neumann-Neumann iterative substructuring methods: Connections and new results, Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods, Deflation and projection methods applied to symmetric positive semi-definite systems, Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems, Automatic spectral coarse spaces for robust finite element tearing and interconnecting and balanced domain decomposition algorithms, Simultaneous FETI and block FETI: Robust domain decomposition with multiple search directions, Implementation of balancing domain decomposition method for parallel finite element analysis involving inactive elements, Balancing Neumann-Neumann methods for the cardiac bidomain model, Fast and accuracy-preserving domain decomposition methods for reduced fracture models with nonconforming time grids, Parallel adaptive solution of 3D boundary value problems by Hessian recovery, Performance comparisons of geometric multigrid solvers and balancing domain decomposition solvers, A unified theory of non-overlapping Robin-Schwarz methods: continuous and discrete, including cross points, BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields, Convergence of linear and nonlinear Neumann-Neumann method for the Cahn-Hilliard equation, Operator Splitting and Local Time-Stepping Methods for Transport Problems in Fractured Porous Media, A Coarse Space to Remove the Logarithmic Dependency in Neumann–Neumann Methods, UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS, Convergence of substructuring methods for the Cahn-Hilliard equation, A numerical study on Neumann-Neumann and FETI methods for \(hp\) approximations on geometrically refined boundary layer meshes in two dimensions., Domain decomposition algorithms for mixed methods for second-order elliptic problems, Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption, The derived-vector space framework and four general purposes massively parallel DDM algorithms, A continuous framework for FETI-DP with a mesh independent condition number for the dual problem, Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps, Space-time domain decomposition for advection-diffusion problems in mixed formulations, A simple and efficient preconditioning scheme for Heaviside enriched XFEM, A Continuous Analysis of Neumann--Neumann Methods: Scalability and New Coarse Spaces, Robust and efficient FETI domain decomposition algorithms for edge element approximations, 2-dimensional primal domain decomposition theory in detail., Multilevel preconditioners for discontinuous Galerkin approximations of elliptic problems with jump coefficients, Heterogeneous domain decomposition method for high contrast dense composites, Fast linear solver for diffusion problems with applications to pressure computation in layered domains, A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations, Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations, Hybrid domain decomposition algorithms for compressible and almost incompressible elasticity, A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions, Two-level preconditioner via a rigid body-based aggregation for the Schur complement system, Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities, An Adaptive MultiPreconditioned Conjugate Gradient Algorithm, A Neumann-Neumann algorithm for a mortar discretization of elliptic problems with discontinuous coefficients, An algebraic theory for primal and dual substructuring methods by constraints, Iterative solvers for coupled fluid-solid scattering, Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation, A balancing Neumann–Neumann method for a mortar finite element discretization of a fourth order elliptic problem, Efficient multigrid solution of elliptic interface problems using viscosity-upwinded local discontinuous Galerkin methods, Domain decomposition for coupled Stokes and Darcy flows, A Discontinuous Coarse Space (DCS) Algorithm for Cell Centered Finite Volume Based Domain Decomposition Methods: The DCS-RJMin Algorithm, A numerical study on Neumann-Neumann methods forhpapproximations on geometrically refined boundary layer meshes II. Three-dimensional problems, Multipliers-free dual-primal domain decomposition methods for nonsymmetric matrices and their numerical testing, An enhanced nonlinear multi-scale strategy for the simulation of buckling and delamination on 3D composite plates, Non-overlapping domain decomposition methods in structural mechanics, Convergence estimates for an optimized Schwarz method for PDEs with discontinuous coefficients, On the use of inexact subdomain solvers for BDDC algorithms, BDDC and FETI-DP without matrices or vectors, Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem, Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions., How to best choose the outer coarse mesh in the domain decomposition method of Bank and Jimack, A Parallel Solver for Large Scale DFN Flow Simulations, Recent Results on Domain Decomposition Preconditioning for the High-Frequency Helmholtz Equation Using Absorption

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A domain decomposition algorithm for elliptic problems in three dimensions
• Domain decomposition methods for large linearly elliptic three-dimensional problems
• Analysis of Preconditioners for Domain Decomposition
• Balancing domain decomposition
• A Taxonomy for Conjugate Gradient Methods
• An Iterative Method for Elliptic Problems on Regions Partitioned into Substructures
• A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• The Interface Probing Technique in Domain Decomposition
• Domain Decomposition Algorithms with Small Overlap
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Balancing Domain Decomposition for Mixed Finite Elements