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dc.contributor.author
Grella, Konstantin
dc.date.accessioned
2022-09-02T09:08:21Z
dc.date.available
2017-06-11T14:43:34Z
dc.date.available
2018-02-15T09:11:02Z
dc.date.available
2022-09-02T09:08:21Z
dc.date.issued
2014-01
dc.identifier.uri
http://hdl.handle.net/20.500.11850/94623
dc.identifier.doi
10.3929/ethz-a-010386299
dc.description.abstract
We develop, analyze, and test a sparse tensor product phase space Galerkin discretization framework for the stationary monochromatic radiative transfer problem with scattering. The mathematical model describes the transport of radiation on a phase space of the Cartesian product of a typically three-dimensional physical domain and two-dimensional angular domain. Known solution methods such as the discrete ordinates method and a spherical harmonics method are derived from the presented Galerkin framework. We construct sparse versions of these well-established methods from the framework and prove that these sparse tensor discretizations break the “curse of dimensionality”: essentially (up to logarithmic factors in the total number of degrees of freedom) the solution complexity increases only as in a problem posed in the physical domain alone, while asymptotic convergence orders in terms of the discretization parameters remain essentially equal to those of a full tensor phase space Galerkin discretization. Algorithmically we compute the sparse tensor approximations by the combination technique. In numerical experiments on 2 + 1 and 3 + 2 dimensional phase spaces we demonstrate that the advantages of sparse tensorization can be leveraged in applications.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
radiative transfer
en_US
dc.subject
sparse grids
en_US
dc.subject
discrete ordinates method
en_US
dc.subject
spherical harmonics method
en_US
dc.subject
combination technique
en_US
dc.title
Sparse tensor phase space Galerkin approximation for radiative transport
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2014-01-25
ethz.journal.title
SAM Research Report
ethz.journal.volume
2014-03
en_US
ethz.size
28 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.grant
Automated Urban Parking and Driving
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
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
en_US
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.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
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=553
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-11T14:43:50Z
ethz.source
ECOL
ethz.source
ECIT
ethz.identifier.importid
imp593652af2691c83336
ethz.identifier.importid
imp59366b6f0ca4478200
ethz.ecolpid
eth:47361
ethz.ecitpid
pub:148573
ethz.eth
yes
en_US
ethz.availability
Open access
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ethz.rosetta.installDate
2017-07-14T22:35:25Z
ethz.rosetta.lastUpdated
2021-02-14T22:22:08Z
ethz.rosetta.exportRequired
true
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true
ethz.COinS
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