Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9506846 | Applied Mathematics and Computation | 2005 | 20 Pages |
Abstract
In this paper, the application of the method of fundamental solutions to the Cauchy problem associated with three-dimensional Helmholtz-type equations is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for under-, equally- and over-determined Cauchy problems in a piecewise smooth geometry. The convergence, accuracy and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Liviu Marin,