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dc.contributor.author
Kazeev, Vladimir
dc.contributor.author
Reichmann, Oleg
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2022-09-08T15:40:19Z
dc.date.available
2017-06-14T01:34:45Z
dc.date.available
2022-09-08T15:40:19Z
dc.date.issued
2012-05
dc.identifier.uri
http://hdl.handle.net/20.500.11850/155040
dc.identifier.doi
10.3929/ethz-a-010406712
dc.description.abstract
We consider the discretization of degenerate, time-inhomogeneous Fokker-Planck equations for diffusion problems in high-dimensional domains. Well-posedness of the problem in time-weighted Bochner spaces is established. Analytic regularity of the time-dependence of the solution in countably normed, weighted Sobolev spaces is established. Time discretization by the hp-discontinuous We consider the discretization of degenerate, time-inhomogeneous Fokker-Planck equations for diffusion problems in high-dimensional domains. Well-posedness of the problem in time-weighted Bochner spaces is established. Analytic regularity of the time-dependence of the solution in countably normed, weighted Sobolev spaces is established. We consider the discretization of degenerate, time-inhomogeneous Fokker-Planck equations for diffusion problems in high-dimensional domains. Well-posedness of the problem in time-weighted Bochner spaces is established. Analytic regularity of the time-dependence of the solution in countably normed, weighted Sobolev spaces is established. Time discretization by the hp-discontinuous Galerkin method is shown to converge exponentially. The resulting elliptic spatial problems are discretized with the use of the tensor-product "hat" finite elements constructed on uniform or patch-wise uniform (Shishkin) meshes and are solved in the Quantized Tensor Train representation. For numerical experiments we consider compatible and incompatible initial data in up to 40 and 18 dimensions respectively on a workstation.
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
Fokker-Planck equation
en_US
dc.subject
degenerate diffusion
en_US
dc.subject
Gevrey regularity
en_US
dc.subject
hp-discontinuous Galerkin
en_US
dc.subject
time stepping
en_US
dc.subject
low-rank representation
en_US
dc.subject
Tensor Train (TT)
en_US
dc.subject
Quantized Tensor Train (QTT)
en_US
dc.title
hp-DG-QTT solution of high-dimensional degenerate diffusion equations
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
SAM Research Report
ethz.journal.volume
2012-11
en_US
ethz.size
31 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
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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
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
en_US
ethz.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=454
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.date.deposited
2017-06-14T01:40:18Z
ethz.source
ECOL
ethz.identifier.importid
imp59366b73c941a65308
ethz.ecolpid
eth:47574
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-18T19:04:57Z
ethz.rosetta.lastUpdated
2024-02-02T18:05:06Z
ethz.rosetta.versionExported
true
ethz.COinS
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