COMPRESSING LARGE-SCALE WAVE PROPAGATION MODELS VIA PHASE-PRECONDITIONED RATIONAL KRYLOV SUBSPACES.
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| Title: | COMPRESSING LARGE-SCALE WAVE PROPAGATION MODELS VIA PHASE-PRECONDITIONED RATIONAL KRYLOV SUBSPACES. |
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| Authors: | DRUSKIN, VLADIMIR1 druskin@slb.com, REMIS, ROB F.2 r.f.remis@tudelft.nl, ZASLAVSKY, MIKHAIL1 mzaslavsky@slb.com, ZIMMERLING, JÖRN T.2 jzimmerl@umich.edu |
| Source: | Multiscale Modeling & Simulation. 2018, Vol. 16 Issue 4, p1486-1518. 33p. |
| Subjects: | Theory of wave motion, High performance computing, Green's functions, Krylov subspace, Acoustic models, Rogue waves |
| Abstract: | Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations where only a few modes contribute to the field. RKS methods, however, are fundamentally limited by the Nyquist--Shannon sampling rate, making them unsuitable for the approximation of wavefields in configuration characterized by large travel times and propagation distances, since wavefield responses in such configurations are highly oscillatory in the frequency-domain. To overcome this limitation, we propose to precondition the RKSs by factoring out the rapidly varying frequency-domain field oscillations. The remaining amplitude-functions are generally slowly varying functions of source position and spatial coordinate and allow for a significant compression of the approximation subspace. Our one-dimensional analysis together with numerical experiments for large-scale two-dimensional acoustic models shows superior approximation properties of preconditioned RKS compared with the standard RKS model-order reduction. The preconditioned RKS results in a reduction of the frequency sampling well below the Nyquist--Shannon rate, a weak dependence of the RKS size on the number of inputs and outputs for multiple-input/multiple-output problems, and, most importantly, in a significant coarsening of the finite-difference grid used to generate the RKS. A prototype implementation indicates that the preconditioned RKS algorithm is competitive in the modern high performance computing environment. [ABSTRACT FROM AUTHOR] |
| Copyright of Multiscale Modeling & Simulation is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 136546669 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: COMPRESSING LARGE-SCALE WAVE PROPAGATION MODELS VIA PHASE-PRECONDITIONED RATIONAL KRYLOV SUBSPACES. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22DRUSKIN%2C+VLADIMIR%22">DRUSKIN, VLADIMIR</searchLink><relatesTo>1</relatesTo><i> druskin@slb.com</i><br /><searchLink fieldCode="AR" term="%22REMIS%2C+ROB+F%2E%22">REMIS, ROB F.</searchLink><relatesTo>2</relatesTo><i> r.f.remis@tudelft.nl</i><br /><searchLink fieldCode="AR" term="%22ZASLAVSKY%2C+MIKHAIL%22">ZASLAVSKY, MIKHAIL</searchLink><relatesTo>1</relatesTo><i> mzaslavsky@slb.com</i><br /><searchLink fieldCode="AR" term="%22ZIMMERLING%2C+JÖRN+T%2E%22">ZIMMERLING, JÖRN T.</searchLink><relatesTo>2</relatesTo><i> jzimmerl@umich.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Multiscale+Modeling+%26+Simulation%22">Multiscale Modeling & Simulation</searchLink>. 2018, Vol. 16 Issue 4, p1486-1518. 33p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22High+performance+computing%22">High performance computing</searchLink><br /><searchLink fieldCode="DE" term="%22Green's+functions%22">Green's functions</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustic+models%22">Acoustic models</searchLink><br /><searchLink fieldCode="DE" term="%22Rogue+waves%22">Rogue waves</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations where only a few modes contribute to the field. RKS methods, however, are fundamentally limited by the Nyquist--Shannon sampling rate, making them unsuitable for the approximation of wavefields in configuration characterized by large travel times and propagation distances, since wavefield responses in such configurations are highly oscillatory in the frequency-domain. To overcome this limitation, we propose to precondition the RKSs by factoring out the rapidly varying frequency-domain field oscillations. The remaining amplitude-functions are generally slowly varying functions of source position and spatial coordinate and allow for a significant compression of the approximation subspace. Our one-dimensional analysis together with numerical experiments for large-scale two-dimensional acoustic models shows superior approximation properties of preconditioned RKS compared with the standard RKS model-order reduction. The preconditioned RKS results in a reduction of the frequency sampling well below the Nyquist--Shannon rate, a weak dependence of the RKS size on the number of inputs and outputs for multiple-input/multiple-output problems, and, most importantly, in a significant coarsening of the finite-difference grid used to generate the RKS. A prototype implementation indicates that the preconditioned RKS algorithm is competitive in the modern high performance computing environment. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Multiscale Modeling & Simulation is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/17M1156848 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 1486 Subjects: – SubjectFull: Theory of wave motion Type: general – SubjectFull: High performance computing Type: general – SubjectFull: Green's functions Type: general – SubjectFull: Krylov subspace Type: general – SubjectFull: Acoustic models Type: general – SubjectFull: Rogue waves Type: general Titles: – TitleFull: COMPRESSING LARGE-SCALE WAVE PROPAGATION MODELS VIA PHASE-PRECONDITIONED RATIONAL KRYLOV SUBSPACES. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: DRUSKIN, VLADIMIR – PersonEntity: Name: NameFull: REMIS, ROB F. – PersonEntity: Name: NameFull: ZASLAVSKY, MIKHAIL – PersonEntity: Name: NameFull: ZIMMERLING, JÖRN T. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: 2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 15403459 Numbering: – Type: volume Value: 16 – Type: issue Value: 4 Titles: – TitleFull: Multiscale Modeling & Simulation Type: main |
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