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dc.contributor.author
Grohs, Philipp
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2017-06-09T16:48:41Z
dc.date.available
2017-06-09T16:48:41Z
dc.date.issued
2011-06
dc.identifier.uri
http://hdl.handle.net/20.500.11850/40051
dc.description.abstract
We propose a novel family of frame discretizations for linear, high-dimensional parametric transport operators. Our approach is based on a least squares formulation in the phase space associated with the transport equation and by subsequent Galerkin discretization with a novel, sparse tensor product frame construction in the possibly high-dimensional phase space. The proposed twisted tensor product frame construction exploits invariance properties of the parameter space under certain group actions and accounts for propagation of singularities. Specically, invariance of the parametric transport operator under rotations of the transport direction. We prove convergence rates of the proposed least squares Galerkin discretizations associated with the twisted tensor frames in terms of the number of degrees of freedom. In particular, sparse versions of the twisted tensor frame constructions are proved to break the curse of dimensionality, also for solution classes with low regularity in isotropic Sobolev spaces due to propagating singularities, uniformly with respect to the propagation directions.
dc.language.iso
en
dc.publisher
Seminar für Angewandte Mathematik, ETH
dc.title
Sparse twisted tensor frame discretization of parametric transport operators
dc.type
Report
ethz.journal.title
Research report
ethz.journal.issue
2011/41
ethz.size
25 p.
ethz.notes
.
ethz.publication.place
Zürich
ethz.publication.status
unpublished
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::03435 - Schwab, Christoph / Schwab, Christoph
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::03435 - Schwab, Christoph / Schwab, Christoph
ethz.identifier.url
http://www.sam.math.ethz.ch/reports/2011/41
ethz.date.deposited
2017-06-09T16:48:46Z
ethz.source
ECIT
ethz.identifier.importid
imp59364e8f1b3b872849
ethz.ecitpid
pub:67168
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-12T17:44:45Z
ethz.rosetta.lastUpdated
2018-10-01T14:01:05Z
ethz.rosetta.versionExported
true
ethz.COinS
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