A domain decomposition algorithm for elliptic problems in three dimensions

DOI10.1007/BF01385722zbMath0724.65110OpenAlexW2107119443MaRDI QIDQ758166

Barry F. Smith

Publication date: 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133592

zbMATH Keywords

finite elementscondition numberthree dimensionsiterative substructuring algorithmpreconditioned conjugate gradientdomain decomposition algorithms

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10)

Related Items (15)

An iterative solver for \(p\)-version finite elements in three dimensions ⋮ Fast domain decomposition algorithm discretizations of 3-d elliptic equations by spectral elements ⋮ Massively parallel methods for semiconductor device modelling ⋮ Iterative methods for \(p\)-version finite elements: Preconditioning thin solids ⋮ Spectral discretizations of 3-D elliptic problems and fast domain decomposition methods ⋮ BDDC and FETI-DP for the virtual element method ⋮ A locally optimal preconditioned Newton-Schur method for symmetric elliptic eigenvalue problems ⋮ FETI-DP for the Three Dimensional Virtual Element Method ⋮ UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS ⋮ Iterative substructuring methods for spectral elements: Problems in three dimensions based on numerical quadrature ⋮ Preconditioners for domain decomposition methods ⋮ Domain decomposition solvers for nonlinear multiharmonic finite element equations ⋮ Substructuring preconditioners for saddle-point problems arising from Maxwell’s equations in three dimensions ⋮ Balancing domain decomposition for problems with large jumps in coefficients ⋮ Parallel adaptive subspace correction schemes with applications to elasticity

Cites Work

• Iterative solvers by substructuring for the \(p\)-version finite element method
• A second order finite difference analog of the first biharmonic boundary value problem
• Two-level domain decomposition preconditioning for thep-version finite element method in three dimensions
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
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