Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation
B. Tomas Johansson; and Liviu Marin;

Source CMC: Computers, Materials, & Continua, Vol. 13, No. 2, pp. 153-190, 2009
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Keywords Helmholtz Equation; Inverse Problem; Cauchy Problem; Alternating Iterative Algorithms; Relaxation Procedure; Boundary Element Method (BEM).
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.
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