|Source||CMC: Computers, Materials, & Continua, Vol. 13, No. 2, pp. 153-190, 2009|
|Download||Full length paper in PDF format. Size = 394,099 bytes|
|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.