Sparse Twisted Tensor Frame Discretization of Parametric Transport Operators
Open access
Datum
2011-06Typ
- Report
ETH Bibliographie
yes
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Abstract
We propose a novel family of frame discretizations for linear, high-dimensional parametric transport operators. Our approach is based on a least squares formulation in the phase space associated with the transport equation and by subsequent Galerkin discretization with a novel, sparse tensor product frame construction in the possibly high-dimensional phase space. The proposed twisted tensor product frame construction exploits invariance properties of the parameter space under certain group actions and accounts for propagation of singularities. Speci cally, invariance of the parametric transport operator under rotations of the transport direction. We prove convergence rates of the proposed least squares Galerkin discretizations associated with the twisted tensor frames in terms of the number of degrees of freedom. In particular, sparse versions of the twisted tensor frame constructions are proved to break the curse of dimensionality, also for solution classes with low regularity in isotropic Sobolev spaces due to propagating singularities, uniformly with respect to the propagation directions. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-a-010406740Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
SAM Research ReportBand
Verlag
Seminar for Applied Mathematics, ETH ZurichOrganisationseinheit
03435 - Schwab, Christoph / Schwab, Christoph
Förderung
247277 - Automated Urban Parking and Driving (EC)
ETH Bibliographie
yes
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