Show simple item record

dc.contributor.author
Hiptmair, Ralf
dc.contributor.author
Moiola, Andrea
dc.contributor.author
Perugia, Ilaria
dc.date.accessioned
2017-06-11T23:32:23Z
dc.date.available
2017-06-11T23:32:23Z
dc.date.issued
2015-06
dc.identifier.uri
http://hdl.handle.net/20.500.11850/111353
dc.description.abstract
Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties of several Trefftz variational formulations developed for the Helmholtz equation, including least squares, discontinuous Galerkin, ultra weak variational formulation, variational theory of complex rays and wave based methods. The most common discrete Trefftz spaces used for this equation employ generalised harmonic polynomials (circular and spherical waves), plane and evanescent waves, fundamental solutions and multipoles as basis functions; we describe theoretical and computational aspects of these spaces, focusing in particular on their approximation properties. One of the most promising, but not yet well developed, features of Trefftz methods is the use of adaptivity in the choice of the propagation directions for the basis functions. The main difficulties encountered in the implementation are the assembly and the ill-conditioning of linear systems, we briefly survey some strategies that have been proposed to cope with these problems.
dc.language.iso
en
dc.publisher
Seminar für Angewandte Mathematik, ETH
dc.title
A Survey of Trefftz Methods for the Helmholtz Equation
dc.type
Report
ethz.journal.title
SAM Research Report
ethz.journal.volume
2015-20
ethz.size
43 p.
ethz.notes
See also: http://e-citations.ethbib.ethz.ch/view/pub:175869.
ethz.publication.place
Zürich
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03632 - Hiptmair, Ralf / Hiptmair, Ralf
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03632 - Hiptmair, Ralf / Hiptmair, Ralf
ethz.identifier.url
http://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-20.pdf
ethz.date.deposited
2017-06-11T23:32:33Z
ethz.source
ECIT
ethz.identifier.importid
imp5936540408b4895261
ethz.ecitpid
pub:172750
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-18T08:11:12Z
ethz.rosetta.lastUpdated
2018-11-02T21:50:51Z
ethz.rosetta.versionExported
true
ethz.COinS
ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.atitle=A%20Survey%20of%20Trefftz%20Methods%20for%20the%20Helmholtz%20Equation&rft.jtitle=SAM%20Research%20Report&rft.date=2015-06&rft.volume=2015-20&rft.au=Hiptmair,%20Ralf&Moiola,%20Andrea&Perugia,%20Ilaria&rft.genre=report&
 Search print copy at ETH Library

Files in this item

FilesSizeFormatOpen in viewer

There are no files associated with this item.

Publication type

Show simple item record