Name
Abstract | ||
|---|---|---|
In this paper, the method of fundamental solutions (MFS) is employed for determining an unknown portion of the boundary from the Cauchy data specified on parts of the boundary. We propose a new numerical method with adaptive placement of source points in the MFS to solve the inverse boundary determination problem. Since the MFS source points placement here is not trivial due to the unknown boundary, we employ an adaptive technique to choose a sub-optimal arrangement of source points on various fictitious boundaries. Afterwards, the standard Tikhonov regularization method is used to solve ill-conditional matrix equation, while the regularization parameter is chosen by the L-curve criterion. The numerical studies of both open and closed fictitious boundaries are considered. It is shown that the proposed method is effective and stable even for data with relatively high noise levels. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2010.07.031 | J. Comput. Physics |
Keywords | Field | DocType |
inverse problem,new numerical method,source point,fictitious boundary,source points placement,mfs source points placement,cauchy data,method of fundamental solutions,standard tikhonov regularization method,various fictitious boundary,adaptive greedy technique,inverse boundary determination problem,adaptive greedy algorithm,unknown boundary,numerical method,tikhonov regularization,greedy algorithm,matrix equation | Tikhonov regularization,Mathematical optimization,Mathematical analysis,Cauchy distribution,Regularization (mathematics),Inverse problem,Method of fundamental solutions,Singular boundary method,Adaptive algorithm,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
229 | 22 | Journal of Computational Physics |
Citations | PageRank | References |
3 | 0.49 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| F. L. Yang | 1 | 3 | 1.17 |
| Leevan Ling | 2 | 145 | 19.59 |
| T. Wei | 3 | 87 | 18.96 |