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dc.contributor.authorImbert-Gerard, L.-M.
dc.date.accessioned2021-07-20T00:11:16Z
dc.date.available2021-07-20T00:11:16Z
dc.date.issued2021
dc.identifier.citationImbert-Gerard, L.-M. (2021). Amplitude-based generalized plane waves: New quasi-trefftz functions for scalar equations in two dimensions. SIAM Journal on Numerical Analysis, 59(3), 1663–1686.
dc.identifier.issn0036-1429
dc.identifier.doi10.1137/20M136791X
dc.identifier.urihttp://hdl.handle.net/10150/660821
dc.description.abstractGeneralized plane waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz property, i.e., they are not exact solutions to the governing equation, they instead satisfy a quasi-Trefftz property: They are only approximate solutions. They lead to high-order numerical methods, and this quasi-Trefftz property is critical for their numerical analysis. The present work introduces a new family of GPWs: amplitude-based. The motivation lies in the poor behavior of the phase-based GPW approximations in the preasymptotic regime, which will be tamed by avoiding high-degree polynomials within an exponential. The new ansatz introduces higher-order terms in the amplitude rather than in the phase of a plane wave as was initially proposed. The new functions' construction and the study of their approximation properties are guided by the road map proposed in [L.-M. Imbert-Gérard and G. Sylvand, Numer. Math., to appear]. For the sake of clarity, the first focus is on the two-dimensional Helmholtz equation with spatially varying wave number. The extension to a range of operators allowing for anisotropy in the first- and second-order terms follows. Numerical simulations illustrate the theoretical study of the new quasi-Trefftz functions. © 2021 Society for Industrial and Applied Mathematics
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics Publications
dc.rightsCopyright © 2021 Society for Industrial and Applied Mathematics.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectBest approximation properties
dc.subjectGeneralized plane waves
dc.subjectQuasi-Trefftz methods
dc.titleAmplitude-based generalized plane waves: New quasi-trefftz functions for scalar equations in two dimensions
dc.typeArticle
dc.typetext
dc.contributor.departmentUniversity of Arizona
dc.identifier.journalSIAM Journal on Numerical Analysis
dc.description.noteImmediate access
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
dc.eprint.versionFinal published version
dc.source.journaltitleSIAM Journal on Numerical Analysis
refterms.dateFOA2021-07-20T00:11:16Z


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