An iterative and parallel solver based on domain decomposition for the \(h-p\) version of the finite element method

DOI10.1016/S0377-0427(97)00063-0zbMath0885.65129MaRDI QIDQ1372118

Weiming Cao, Ben Qi Guo

Publication date: 2 April 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

preconditioningparallel computationcondition numberiterative methodsh-p version of the finite element method

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05)

Related Items

Three-dimensional generalized inverse matrix rational interpolation, Efficient parallel implementations of finite element methods based on the conjugate gradient method, A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods, Some algebraic properties of generalized inverse matrix-valued Padé approximation, Sparse shape functions for tetrahedral \(p\)-FEM using integrated Jacobi polynomials, Generalized inverse vector valued osculatory rational interpolation and its error formula, Error estimates and adaptive finite element methods, Optimal extensions on tensor-product meshes, A domain decomposition preconditioner for \(p\)-FEM discretizations of two-dimensional elliptic problems, New shape functions for triangular \(p\)-FEM using integrated Jacobi polynomials, FEM and BEM parallel processing: theory and applications – a bibliography (1996‐2002), The ε-algorithm and η-algorithm for generalized inverse rectangular matrix pade approximants

Cites Work

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• Iterative substructuring methods for spectral elements: Problems in three dimensions based on numerical quadrature
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• Iterative solvers by substructuring for the \(p\)-version finite element method
• A preconditioner for the \(h\)-\(p\) version of the finite element method in two dimensions
• The problem of selecting the shape functions for ap-type finite element
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Iterative Methods by Space Decomposition and Subspace Correction
• Domain Decomposition Algorithms with Small Overlap
• Additive Schwarz Methods for the h-p Version of the Finite Element Method in Two Dimensions
• An Additive Schwarz Method for the h-p Version of the Finite Element Method in Three Dimensions
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
• A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions
• A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes