Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators

Language

English

Abstract

In this paper we combine the method of fundamental solutions with various regularization techniques to solve Cauchy problems of elliptic differential operators. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. To solve effectively the discrete ill-posed resultant matrix, we use three regularization strategies under three different choices for the regularization parameter. Several examples on problems with smooth and non-smooth geometries in 2D and 3D spaces using under-, equally, and over-specified Cauchy data on an accessible boundary are given. Numerical results indicate that the generalized cross-validation and L-curve choice rulers for Tikhonov regularization and damped singular value decomposition strategy are most effective when using the same numbers of collocation and source points. It has also been observed that the use of more Cauchy data will greatly improve the accuracy of the approximate solution. © 2006.

Keywords

Cauchy problems, Inverse problems, Method of fundamental solutions, Regularization methods

Publication Date

2007

Source Publication Title

Engineering Analysis with Boundary Elements

Volume

31

Issue

4

Start Page

373

End Page

385

Publisher

Elsevier

DOI

10.1016/j.enganabound.2006.07.010

ISSN (print)

09557997

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