The approximate Dirichlet domain decomposition method. I: An algebraic approach

DOI10.1007/BF02253431zbMath0741.65091OpenAlexW154172017MaRDI QIDQ1180345

Gundolf Haase, Ulrich Langer, Arnd Meyer

Publication date: 27 June 1992

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02253431

zbMATH Keywords

finite elementsdomain decompositionparallel algorithmspreconditionerselliptic problemssubstructuring

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) Parallel numerical computation (65Y05)

Related Items

Unnamed Item, Hierarchical extension operators plus smoothing in domain decomposition preconditioners, Parallel frequency filtering, Parallel solvers for linear and nonlinear exterior magnetic field problems based upon coupled FE/BE formulations, A p‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen, A three-level BDDC algorithm for a saddle point problem, \(\mathrm{FE}^2\) multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition, The approximate Dirichlet domain decomposition method. II: Applications to 2nd-order elliptic B.V.P.s, A Brief History of the Parallel Dawn in Karl-Marx-Stadt/Chemnitz, Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes, Exploiting thread-level parallelism in the iterative solution of sparse linear systems, Optimal extensions on tensor-product meshes, A domain decomposition preconditioner for \(p\)-FEM discretizations of two-dimensional elliptic problems, A parallel mixed finite element implementation of fourth-order plate bending problems in distributed memory environments, Domain decomposition solvers for nonlinear multiharmonic finite element equations, Solving the Signorini problem on the basis of domain decomposition techniques, On the use of inexact subdomain solvers for BDDC algorithms, Unnamed Item, A Note on the Global Extraction Element‐by‐Element Method

Cites Work

• A finite element - capacitance method for elliptic problems on regions partitioned into subregions
• A fast iterative method for solving stationary heat conduction problems on regions partitioned into rectangles
• The Neumann-Dirichlet domain decomposition method with inexact solvers on the subdomains
• A capacitance matrix method for Dirichlet problem on polygon region
• The approximate Dirichlet domain decomposition method. II: Applications to 2nd-order elliptic B.V.P.s
• A parallel preconditioned conjugate gradient method using domain decomposition and inexact solvers on each subdomain
• A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• TRIANGULAR PLATE ELEMENTS IN THE MATRIX FORCE METHOD OF STRUCTURAL ANALYSIS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item