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Section: New Results

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

Participant : Angelos Mantzaflaris.

In [14] 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.

This work was done jointly with F. Scholz and I. Toulopoulos (RICAM - Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria).