<> <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/10071583> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/AcademicArticle> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/dc/terms/title> "Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/ontology/bibo/abstract> "A new, coercive formulation of the Helmholtz equation was introduced in [1]. In this paper we\r\ninvestigate h-version Galerkin discretisations of this formulation, and the iterative solution of the\r\nresulting linear systems. We find that the coercive formulation behaves similarly to the standard\r\nformulation in terms of the pollution effect (i.e. to maintain accuracy as k → ∞, h must decrease\r\nwith k at the same rate as for the standard formulation). We prove k-explicit bounds on the\r\nnumber of GMRES iterations required to solve the linear system of the new formulation when it\r\nis preconditioned with a prescribed symmetric positive-definite matrix. Even though the number\r\nof iterations grows with k, these are the first such rigorous bounds on the number of GMRES\r\niterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is\r\na symmetric positive-definite matrix."^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/dc/terms/date> "2019-05-15" . <https://discovery.ucl.ac.uk/id/document/878199> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/ontology/bibo/volume> "352" . <https://discovery.ucl.ac.uk/id/org/ext-9ecf5daebd7d82811c8e164b3c84a874> <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-9ecf5daebd7d82811c8e164b3c84a874> <http://xmlns.com/foaf/0.1/name> "ELSEVIER SCIENCE BV"^^<http://www.w3.org/2001/XMLSchema#string> . 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<http://purl.org/ontology/bibo/status/published> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-8f1102b5f100006914c6027f80324df6> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> . <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_1> <https://discovery.ucl.ac.uk/id/person/ext-8f1102b5f100006914c6027f80324df6> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-f24490955d4539ba2e58371818917126> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> . <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_2> <https://discovery.ucl.ac.uk/id/person/ext-f24490955d4539ba2e58371818917126> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/dc/terms/creator> <https://discovery.ucl.ac.uk/id/person/ext-eea1d1ed575d99a9ad45666ed16239d8> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://purl.org/ontology/bibo/authorList> <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> . <https://discovery.ucl.ac.uk/id/eprint/10071583#authors> <http://www.w3.org/1999/02/22-rdf-syntax-ns#_3> <https://discovery.ucl.ac.uk/id/person/ext-eea1d1ed575d99a9ad45666ed16239d8> . <https://discovery.ucl.ac.uk/id/person/ext-f24490955d4539ba2e58371818917126> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Person> . <https://discovery.ucl.ac.uk/id/person/ext-f24490955d4539ba2e58371818917126> <http://xmlns.com/foaf/0.1/givenName> "A"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/person/ext-f24490955d4539ba2e58371818917126> 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(Other)"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/document/878201> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/document/878201> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/document/878201> <http://eprints.org/relation/ispreviewThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/878202> . <https://discovery.ucl.ac.uk/id/document/878202> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> . <https://discovery.ucl.ac.uk/id/document/878202> <http://www.w3.org/2000/01/rdf-schema#label> "Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? (Other)"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/document/878202> <http://eprints.org/relation/isVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/document/878202> <http://eprints.org/relation/isVolatileVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/document/878202> <http://eprints.org/relation/ismediumThumbnailVersionOf> <https://discovery.ucl.ac.uk/id/document/878199> . <https://discovery.ucl.ac.uk/id/eprint/10071583> <http://eprints.org/ontology/hasDocument> <https://discovery.ucl.ac.uk/id/document/878203> . <https://discovery.ucl.ac.uk/id/document/878203> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://eprints.org/ontology/Document> . <https://discovery.ucl.ac.uk/id/document/878203> <http://www.w3.org/2000/01/rdf-schema#label> "Can coercive formulations lead to fast and accurate solution of the Helmholtz equation? 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