Residual cutting method for elliptic boundary value problems: Application to Poisson's equation
type: Item
instance of: scholarly article
title: Residual cutting method for elliptic boundary value problems: Application to Poisson's equation
zbMATH Open document ID: 0888.65111
author: Atsuhiro Tamura
author: Kazuo Kikuchi
author: T. Takahashi
published in: Journal of Computational Physics
publication date: 1998-05-12T00:00:00Z
review text: The paper is concerned with an iterative solver for elliptic boundary value problems. The main idea of the method is to present the current solutions increments as a linear combination of the approximate solution of the corresponding residual equation obtained as a result of \(M\) internal iterations and increments corresponding to \(L\) previous iterations. The coefficients of the combination (the residual cutting coefficients) are then determined as the least squares solutions of the next residual equation. It is proved that the process converges if some not very restrictive condition is met. Computational examples for the Poisson equation showing fast convergence with relatively small values of \(M\) and \(L\) are presented. The application of the method to ill-posed Neumann problems is discussed and demonstrated.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1100736
zbMATH Keywords: elliptic boundary value problems
zbMATH Keywords: iterative methods
zbMATH Keywords: least squares solutions
zbMATH Keywords: Poisson equation
zbMATH Keywords: Neumann problem
zbMATH Keywords: residual cutting method
zbMATH Keywords: convergence
reviewed by: A. I. Tolstykh
MaRDI profile type: Publication
full work available at URL: jcph.1997.5807
OpenAlex ID: W2027305902
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DOI: 10.1006/JCPH.1997.5807
description: scientific article; zbMATH DE number 1100736