Snapshot Location by Error Equilibration in Proper Orthogonal Decomposition for Linear and Semilinear Parabolic Partial Differential Equations

  • It is well-known that the performance of snapshot based POD and POD-DEIM for spatially semidiscretized parabolic PDEs depends on the proper selection of the snapshot locations. In this contribution, we present an approach that for a fixed number of snapshots selects the location based on error equilibration in the sense that the global discretization error is approximately the same in each associated subinterval. The global discretization error is assessed by a hierarchical-type a posteriori error estimator known from automatic time-stepping for systems of ODEs. We study the impact of this snapshot selection on error equilibration for the ROM and provide numerical examples that illustrate the performance of the suggested approach.

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Author:Ronald H. W. HoppeORCiDGND, Zhiheng Liu
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-21)
Publishing Institution:Universität Augsburg
Release Date:2013/11/06
Tag:snapshot location; proper orthogonal decomposition; discrete empirical interpolation method; error equilibration; semilinear parabolic equations; model reduction
GND-Keyword:Ordnungsreduktion; Parabolische Differentialgleichung; Orthogonale Zerlegung; A-posteriori-Abschätzung; Finite-Elemente-Methode
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand