An accelerated domain decomposition procedure based on Robin transmission conditions
type: Item
instance of: scholarly article
title: An accelerated domain decomposition procedure based on Robin transmission conditions
zbMATH Open document ID: 0886.65114
DOI: 10.1007/BF02510246
published in: BIT
publication date: 1998-04-14T00:00:00Z
review text: An accelerated domain decomposition procedure based on Robin transmission conditions is considered. A new method of convergence acceleration is proposed for some model problems. This method is more effective than that proposed by P. L. Lions. The model boundary value problem \[ -\Delta u= f,\quad x \in \Omega;\qquad u =0,\quad x \in \partial\Omega, \] where the domain \(\Omega=(-\infty,\infty) \times (0,1)\) is the unit strip, is considered. Under reasonable conditions the model problem is equivalent to solving the two problems \[ -\Delta u_i= f,\quad x\in \Omega_i;\qquad u_i=0, \quad x \in \partial\Omega \cap \partial\Omega_i, \quad i=1,2 \] subject to two consistency conditions. Test examples for two- and three-dimensional problems are considered. The results of computation are consistent with the theoretical estimates. Problems of realization for the proposed procedure are considered, too.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1087024
zbMATH Keywords: Poisson equation
zbMATH Keywords: numerical examples
zbMATH Keywords: Robin transmission condition
zbMATH Keywords: accelerated domain decomposition procedure
zbMATH Keywords: convergence acceleration
author: Jim jun. Douglas
author: Chieh-Sen Huang
reviewed by: Peter P. Matus
MaRDI profile type: Publication
cites work: A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods
full work available at URL: https://doi.org/10.1007/bf02510246
OpenAlex ID: W1987240068
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description: scientific article; zbMATH DE number 1087024