<> <http://www.w3.org/2000/01/rdf-schema#comment> "The repository administrator has not yet configured an RDF license."^^<http://www.w3.org/2001/XMLSchema#string> . <> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10185834> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/AcademicArticle> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://purl.org/dc/terms/title> "The hp-FEM applied to the Helmholtz equation with PML\r\ntruncation does not suffer from the pollution effect"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://purl.org/ontology/bibo/abstract> "We consider approximation of the variable-coefficient Helmholtz equation in the exterior of a Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known that this approximation is exponentially accurate in the PML width and the scaling angle, and the approximation was recently proved to be exponentially accurate in the wavenumber k in [28]. We show that the hp-FEM applied to this problem does not suffer from the pollution effect, in that there exist C1, C2 > 0 such that if hk/p ≤ C1 and p ≥ C2 log k then the Galerkin solutions are quasioptimal (with constant independent of k), under the following two conditions (i) the solution operator of the original Helmholtz problem is polynomially bounded in k (which occurs for “most†k by [41]), and (ii) either there is no obstacle and the coefficients are smooth or the obstacle is analytic and the coefficients are analytic in a neighbourhood of the obstacle and smooth elsewhere. This hp-FEM result is obtained via a decomposition of the PML solution into “high-†and “low-frequency†components, analogous to the decomposition for the original Helmholtz solution recently proved in [29]. The decomposition is obtained using tools from semiclassical analysis (i.e., the PDE techniques specifically designed for studying Helmholtz problems with large k)."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://purl.org/dc/terms/date> "2024" . <https://discovery.ucl.ac.uk/id/document/1684764> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://purl.org/ontology/bibo/volume> "22" . <https://discovery.ucl.ac.uk/id/eprint/10185834> <http://purl.org/ontology/bibo/issue> "7" . <https://discovery.ucl.ac.uk/id/org/ext-0b07542fc7d02831c9d95122c8503198> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Organization> . <https://discovery.ucl.ac.uk/id/org/ext-0b07542fc7d02831c9d95122c8503198> <http://xmlns.com/foaf/0.1/name> "International Press of Boston, Inc."^^<http://www.w3.org/2001/XMLSchema#string> . 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