On the existence and convergence of the solution of PML equations |
| |
Authors: | Matti Lassas Erkki Somersalo |
| |
Affiliation: | (1) Rolf Nevanlinna Institute, University of Helsinki, P.O. Box 4, FIN-00014, Finland;(2) Department of Mathematics, Helsinki University of Technology, Otakaari 1, FIN-02150 Espoo, Finland |
| |
Abstract: | In this article we study the mesh termination method in computational scattering theory known as the method of Perfectly Matched
Layer (PML). This method is based on the idea of surrounding the scatterer and its immediate vicinity with a fictitious absorbing
non-reflecting layer to damp the echoes coming from the mesh termination surface. The method can be formulated equivalently
as a complex stretching of the exterior domain. The article is devoted to the existence and convergence questions of the solutions
of the resulting equations. We show that with a special choice of the fictitious absorbing coefficient, the PML equations
are solvable for all wave numbers, and as the PML layer is made thicker, the PML solution converge exponentially towards the
actual scattering solution. The proofs are based on boundary integral methods and a new type of near-field version of the
radiation condition, called here the double surface radiation condition.
Partly supported by the Finnish Academy, project 37692. |
| |
Keywords: | 35J05 65N12 78A40 |
本文献已被 SpringerLink 等数据库收录! |
|