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dc.contributor.authorDemanet, Laurent
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2010-03-22T13:21:34Z
dc.date.available2010-03-22T13:21:34Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3750
dc.language.isoenen
dc.subjectwave equationen
dc.subjectCompressed samplingen
dc.subjectcompressed sensingen
dc.subjectsparsityen
dc.subjectL1en
dc.subjectcompressive sensingen
dc.subject.ddc520en
dc.titleCompressive Wave Computationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen at random, and that this provides a natural way of parallelizing wave simulations for memory-intensive applications. This paper shows that L1-Helmholtz recovery makes sense for wave computation, and identifies a regime in which it is provably effective: the one-dimensional wave equation with coefficients of small bounded variation. Under suitable assumptions we show that the number of eigenfunctions needed to evolve a sparse wavefield defined on N points, accurately with very high probability, is bounded by C log(N) log(log(N)), where C is related to the desired accuracy and can be made to grow at a much slower rate than N when the solution is sparse. The PDE estimates that underlie this result are new to the authors' knowledge and may be of independent mathematical interest; they include an L1 estimate for the wave equation, an estimate of extension of eigenfunctions, and a bound for eigenvalue gaps in Sturm-Liouville problems. Numerical examples are presented in one spatial dimension and show that as few as 10 percents of all eigenfunctions can suffice for accurate results. Finally, we argue that the compressive viewpoint suggests a competitive parallel algorithm for an adjoint-state inversion method in reflection seismology.en
dc.relation.isversionofjnlnameFoundations of Computational Mathematics
dc.relation.isversionofjnlvol11
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages257-303
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10208-011-9085-5
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00368919/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelSciences connexes (physique, astrophysique)en


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