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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 19, Issue 1

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

Angelos Mantzaflaris
/ Felix Scholz
/ Ioannis Toulopoulos
• Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria
• Email
• Other articles by this author:
Published Online: 2018-07-07 | DOI: https://doi.org/10.1515/cmam-2018-0024

## Abstract

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 ${ℝ}^{d+1}$, 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.

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

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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,

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