On the existence and convergence of the solution of PML equations

@article{citeulike:2425582, abstract = {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.}, author = {Lassas, Matti and Somersalo, Erkki }, citeulike-article-id = {2425582}, doi = {http://dx.doi.org/10.1007/BF02684334}, journal = {Computing}, keywords = {helmholtz, pml, uniqueness-existence}, number = {3}, pages = {229--241}, posted-at = {2008-02-25 13:35:25}, priority = {4}, title = {On the existence and convergence of the solution of PML equations}, url = {http://dx.doi.org/10.1007/BF02684334}, volume = {60}, year = {1998} }

TY - JOUR ID - citeulike:2425582 L3 - citeulike-article-id:2425582 TI - On the existence and convergence of the solution of PML equations JF - Computing VL - 60 IS - 3 SP - 229 EP - 241 N2 - 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. KW - helmholtz KW - pml KW - uniqueness-existence AU - Lassas, Matti AU - Somersalo, Erkki PY - 1998/// UR - http://dx.doi.org/10.1007/BF02684334 ER -