B. Tomas Johansson1, Liviu Marin2
CMC-Computers, Materials & Continua, Vol.13, No.2, pp. 153-190, 2009, DOI: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. More >
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