Open Access

ARTICLE

Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation

B. Tomas Johansson¹, Liviu Marin²

1 School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. E-mail: b. t. johansson@bham.ac.uk
2 Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, P.O. Box 1-863, 010141 Bucharest, Romania. E-mails: marin.liviu@gmail.com; liviu@imsar.bu.edu.ro

Computers, Materials & Continua 2009, 13(2), 153-190. https://doi.org/10.3970/cmc.2009.013.153

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 Kozlov, Maz'ya and Fomin(1991) 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.

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