Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients

Angelos Mantzaflaris (1, 2, 3) , Felix Scholz (3) , Ioannis Toulopoulos (3)

1 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
3 RICAM - Johann Radon Institute for Computational and Applied Mathematics

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 +1 , with = 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.

Mots clés: Isogeometric Analysis; low-rank approximation; parabolic initial-boundary value problems; B-splines; isogeometric matrix assembly

Domaines: Analyse numérique [math.NA]; Modélisation et simulation; Calcul formel [cs.SC]

Angelos Mantzaflaris, Felix Scholz, Ioannis Toulopoulos. Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients. Computational Methods in Applied Mathematics, 2019, 19 (1), pp.123-136. ⟨10.1515/cmam-2018-0024⟩. ⟨hal-02271808⟩