TY - EJOU
AU - Johansson, B. Tomas
AU - Marin, Liviu
TI - Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation
T2 - Computers, Materials \& Continua
PY - 2009
VL - 13
IS - 2
SN - 1546-2226
AB - 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.
KW - Helmholtz Equation
KW - Inverse Problem
KW - Cauchy Problem
KW - Alternating Iterative Algorithms
KW - Relaxation Procedure
KW - Boundary Element Method (BEM)
DO - 10.3970/cmc.2009.013.153