Implementation and application of explicit SSP multi-rate time integration methods in PETSc
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| Názov: | Implementation and application of explicit SSP multi-rate time integration methods in PETSc |
|---|---|
| Autori: | Zhang, Hong |
| Informácie o vydavateľovi: | Banff International Research Station for Mathematical Innovation and Discovery |
| Rok vydania: | 2018 |
| Zbierka: | University of British Columbia: cIRcle - UBC's Information Repository |
| Predmety: | Mathematics, Numerical analysis, Partial differential equations, Scientific computing |
| Geografické téma: | Banff (Alta.) |
| Popis: | Multirate time integration methods allow for adaptation of local time step size, are thus particularly efficient for multi-scale systems that have widely different time scale characteristics. However, classic multi-rate schemes designed for ODEs are typically difficult to be extended for PDEs because of additional stability requirements. For example, hyperbolic conservation laws require the numerical schemes to be positivity-preserving and total variation diminishing. While multi-rate partitioned Runge-Kutta methods were proposed to use different time steps on different grid cells to overcome the global CFL constraint, buffer regions have to be introduced in order to accommodate the transition between subdomains. Implementation of these methods are tricky and highly application-dependent, and especially challenging for general-purpose libraries. In this talk, we will present our recent development of multi-rate time integrators in PETSc, which is one of the most popular software library for the scalable solution of scientific applications modeled by PDEs. We will introduce the new data structure support for componentwise partitioned systems that arise naturally from mesh refinement, and show how the serial and parallel efficiency is achieved. To illustrate the capability of the PETSc multi-rate integrators for hyperbolic conservation laws, we will focus on the advection equation solved using conservative finite volume methods with consistent slope limiters. ; Non UBC ; Unreviewed ; Author affiliation: Argonne National Laboratory ; Other |
| Druh dokumentu: | moving image (video) |
| Popis súboru: | 31.0; video/mp4 |
| Jazyk: | English |
| Relation: | 18w5152: Integrating the Integrators for Nonlinear Evolution Equations: from Analysis to Numerical Methods, High-Performance-Computing and Applications; BIRS Workshop Lecture Videos (Banff, Alta); BIRS-VIDEO-201812061613-Zhang; BIRS-VIDEO-18w5152-30724; http://hdl.handle.net/2429/70509 |
| Dostupnosť: | http://hdl.handle.net/2429/70509 |
| Rights: | Attribution-NonCommercial-NoDerivatives 4.0 International ; http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Prístupové číslo: | edsbas.90A0F6CD |
| Databáza: | BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: Implementation and application of explicit SSP multi-rate time integration methods in PETSc – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Hong%22">Zhang, Hong</searchLink> – Name: Publisher Label: Publisher Information Group: PubInfo Data: Banff International Research Station for Mathematical Innovation and Discovery – Name: DatePubCY Label: Publication Year Group: Date Data: 2018 – Name: Subset Label: Collection Group: HoldingsInfo Data: University of British Columbia: cIRcle - UBC's Information Repository – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+computing%22">Scientific computing</searchLink> – Name: Subject Label: Subject Geographic Group: Su Data: <searchLink fieldCode="DE" term="%22Banff+%28Alta%2E%29%22">Banff (Alta.)</searchLink> – Name: Abstract Label: Description Group: Ab Data: Multirate time integration methods allow for adaptation of local time step size, are thus particularly efficient for multi-scale systems that have widely different time scale characteristics. However, classic multi-rate schemes designed for ODEs are typically difficult to be extended for PDEs because of additional stability requirements. For example, hyperbolic conservation laws require the numerical schemes to be positivity-preserving and total variation diminishing. While multi-rate partitioned Runge-Kutta methods were proposed to use different time steps on different grid cells to overcome the global CFL constraint, buffer regions have to be introduced in order to accommodate the transition between subdomains. Implementation of these methods are tricky and highly application-dependent, and especially challenging for general-purpose libraries. In this talk, we will present our recent development of multi-rate time integrators in PETSc, which is one of the most popular software library for the scalable solution of scientific applications modeled by PDEs. We will introduce the new data structure support for componentwise partitioned systems that arise naturally from mesh refinement, and show how the serial and parallel efficiency is achieved. To illustrate the capability of the PETSc multi-rate integrators for hyperbolic conservation laws, we will focus on the advection equation solved using conservative finite volume methods with consistent slope limiters. ; Non UBC ; Unreviewed ; Author affiliation: Argonne National Laboratory ; Other – Name: TypeDocument Label: Document Type Group: TypDoc Data: moving image (video) – Name: Format Label: File Description Group: SrcInfo Data: 31.0; video/mp4 – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: 18w5152: Integrating the Integrators for Nonlinear Evolution Equations: from Analysis to Numerical Methods, High-Performance-Computing and Applications; BIRS Workshop Lecture Videos (Banff, Alta); BIRS-VIDEO-201812061613-Zhang; BIRS-VIDEO-18w5152-30724; http://hdl.handle.net/2429/70509 – Name: URL Label: Availability Group: URL Data: http://hdl.handle.net/2429/70509 – Name: Copyright Label: Rights Group: Cpyrght Data: Attribution-NonCommercial-NoDerivatives 4.0 International ; http://creativecommons.org/licenses/by-nc-nd/4.0/ – Name: AN Label: Accession Number Group: ID Data: edsbas.90A0F6CD |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: Banff (Alta.) Type: general – SubjectFull: Mathematics Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Scientific computing Type: general Titles: – TitleFull: Implementation and application of explicit SSP multi-rate time integration methods in PETSc Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Hong IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2018 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
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