An Optimal Two-Level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions

DOI10.1137/0914014zbMath0771.65083OpenAlexW1980588520MaRDI QIDQ5286345

Xiao-Chuan Cai

Publication date: 29 June 1993

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

Full work available at URL: https://semanticscholar.org/paper/771e064980a7272e44870cd8f4fee2a40ce83eeb

zbMATH Keywords

convergenceiterative methodgeneralized minimal residual methodmultiplicative Schwarz algorithmadditive Schwarz algorithmelliptic finite element problemstwo-level overlapping domain decompositionGMRES parallel computation

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 (9)

Numerical solution of nonlinear differential boundary value problems using adaptive non-overlapping domain decomposition method ⋮ Stochastic domain decomposition based on variable-separation method ⋮ A novel domain decomposition framework for the ground state solution of Bose-Einstein condensates ⋮ Solving the nonlinear and nonstationary Richards equation with two-level adaptive domain decomposition (\(dd\)-adaptivity) ⋮ Theoretical and numerical analysis of a class of quasilinear elliptic equations ⋮ Two-grid algorithms for some linear and nonlinear elliptic systems ⋮ Numerical analysis of the rectangular domain decomposition method ⋮ Optimized Schwarz methods without overlap for highly heterogeneous media ⋮ An efficient domain decomposition method for three-dimensional parabolic problems

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