Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

B. Tomas Johansson, Liviu Marin

Research output: Contribution to journalArticle

Abstract

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.
Original languageEnglish
Pages (from-to)153-190
Number of pages37
JournalComputers Materials and Continua
Volume13
Issue number2
DOIs
Publication statusPublished - 2009

Keywords

  • Helmholtz equation
  • inverse problem
  • Cauchy problem
  • alternating iterative algorithms
  • relaxation procedure
  • boundary element method

Fingerprint Dive into the research topics of 'Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation'. Together they form a unique fingerprint.

  • Cite this