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Computational Methods in Applied Mathematics

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Volume 19, Issue 1


Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients

Angelos MantzaflarisORCID iD: https://orcid.org/0000-0001-7135-1084 / Felix ScholzORCID iD: https://orcid.org/0000-0003-3339-0079 / Ioannis Toulopoulos
  • Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria
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Published Online: 2018-07-07 | DOI: https://doi.org/10.1515/cmam-2018-0024


In this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in d+1, with d=2,3, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.

Keywords: Isogeometric Analysis; Low-Rank Approximation; Parabolic Initial-Boundary Value Problems; B-Splines; Isogeometric Matrix Assembly

MSC 2010: 65D07; 65M12; 65M15; 65M60


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About the article

Received: 2017-10-10

Revised: 2018-01-16

Accepted: 2018-05-02

Published Online: 2018-07-07

Published in Print: 2019-01-01

Funding Source: Austrian Science Fund

Award identifier / Grant number: NFN S117

This work was supported by the Austrian Science Fund (FWF) under the grant NFN S117.

Citation Information: Computational Methods in Applied Mathematics, Volume 19, Issue 1, Pages 123–136, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0024.

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