Multi-level Monte Carlo finite difference and finite volume methods for stochastic linear hyperbolic systems
dc.contributor.author
Šukys, Jonas
dc.contributor.author
Schwab, Christoph
dc.contributor.author
Mishra, Siddhartha
dc.date.accessioned
2022-09-19T08:11:16Z
dc.date.available
2022-09-19T08:11:16Z
dc.date.issued
2012-07
dc.identifier.uri
http://hdl.handle.net/20.500.11850/571297
dc.identifier.doi
10.3929/ethz-a-010395433
dc.description.abstract
We consider stochastic multi-dimensional linear hyperbolic systems of conservation laws. We prove existence and uniqueness of a random weak solution, provide estimates for the regularity of the solution in terms of regularities of input data, and show existence of statistical moments. Bounds for mean square error vs. expected work are proved for the Multi-Level Monte Carlo Finite Volume algorithm which is used to approximate the moments of the solution. Using our implementation called ALSVID-UQ, numerical experiments for acoustic wave equation with uncertain uniformly and log-normally distributed coefficients are conducted.
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dc.format
application/pdf
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dc.language.iso
en
en_US
dc.publisher
Seminar for Applied Mathematics, ETH Zurich
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dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.title
Multi-level Monte Carlo finite difference and finite volume methods for stochastic linear hyperbolic systems
en_US
dc.type
Report
dc.rights.license
In Copyright - Non-Commercial Use Permitted
ethz.journal.title
SAM Research Report
ethz.journal.volume
2012-19
en_US
ethz.size
18 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::510 - Mathematics
en_US
ethz.grant
Automated Urban Parking and Driving
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ethz.publication.place
Zurich
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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
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::03851 - Mishra, Siddhartha / Mishra, Siddhartha
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::03851 - Mishra, Siddhartha / Mishra, Siddhartha
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.identifier.url
https://math.ethz.ch/sam/research/reports.html?id=462
ethz.grant.agreementno
247277
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
FP7
ethz.relation.isPreviousVersionOf
20.500.11850/79163
ethz.date.deposited
2017-06-10T11:38:20Z
ethz.source
ECIT
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ECOL
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imp59366b7091fdc87011
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imp593650291a9ce53673
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eth:47432
ethz.ecitpid
pub:94790
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pub:97084
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yes
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ethz.availability
Open access
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ethz.rosetta.installDate
2022-09-19T08:11:25Z
ethz.rosetta.lastUpdated
2023-02-07T06:23:09Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/154957
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/59265
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/60791
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