The boundary element method for the solution of the backward heat conduction equation
type: Item
instance of: scholarly article
title: The boundary element method for the solution of the backward heat conduction equation
zbMATH Open document ID: 0821.65064
author: Houde Han
author: Y. Yuan
author: Derek B. Ingham
published in: Journal of Computational Physics
publication date: 1995-04-05T00:00:00Z
review text: In an earlier paper the same authors introduced the boundary element method modified with a minimal energy scheme to solve the Laplace equation with insufficient boundary data. Here this method is extended to solve the backward unsteady heat conduction problem. This problem is improperly posed, therefore neither the direct solution of the linear system obtained by discretisation nor the least squares solution is possible. It is necessary to add restrictions. The problem is reformulated and an energy functional \(J(u)\) is minimized additionally. Three choices for \(J(u)\) are considered, but for different reasons only the simplest possibility \(J(u) = \int^ 1_ 0 u^ 2 (x,0) dx\) is used for the presented results. These results show that the method is very robust, and that a good initial guess is not important. An alternative method using a time- marching scheme is being investigated by the authors to reduce the large amount of computer storage.
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 740631
zbMATH Keywords: improperly posed problem
zbMATH Keywords: energy method
zbMATH Keywords: boundary element method
zbMATH Keywords: backward unsteady heat conduction problem
zbMATH Keywords: time-marching scheme
MaRDI profile type: Publication
full work available at URL: jcph.1995.1028
OpenAlex ID: W1996644894
DOI: 10.1006/JCPH.1995.1028
description: scientific article; zbMATH DE number 740631