Composite iterative method for elliptic problems in irregular regions
type: Item
instance of: scholarly article
title: Composite iterative method for elliptic problems in irregular regions
zbMATH Open document ID: 0702.65087
DOI: 10.1016/0168-9274(90)90020-G
published in: Applied Numerical Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A finite element piecewise linear approximation with triangular elements to a self-adjoint second-order elliptic equation in an irregular bounded two-dimensional region with Dirichlet boundary condition is considered. A composite inner-outer iterations method for the arising linear system of algebraic equations is presented. Preconditioned Richardson iterations are chosen as the outer iterations, in which the discrete Laplacian is employed as a preconditioner. In each outer iteration systems with the Laplacian in an irregular region are solved by the imbedding capacitance matrix method that uses conjugate gradients as the inner iterations. The inner iterations are terminated before they have converged to full accuracy. The authors prove that with an optimal control of the termination criterion for inner iterations the rate of convergence of this composite iterative process depends only logarithmically on h, the parameter of triangulation. Numerical examples are shown.
reviewed by: L.Boubelíková
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4151773
zbMATH Keywords: finite element
zbMATH Keywords: self-adjoint second-order elliptic equation
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: composite inner-outer iterations method
zbMATH Keywords: Preconditioned Richardson iterations
zbMATH Keywords: preconditioner
zbMATH Keywords: capacitance matrix method
zbMATH Keywords: conjugate gradients
zbMATH Keywords: termination criterion
zbMATH Keywords: rate of convergence
zbMATH Keywords: Numerical examples
author: Maksymilian Dryja
author: Wlodek Proskurowski
MaRDI profile type: Publication
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full work available at URL: 0168-9274(90)90020-g
OpenAlex ID: W1988095094
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description: scientific article; zbMATH DE number 4151773