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

Angelos Mantzaflaris*, Felix Scholz, Ioannis Toulopoulos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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 Rd+1, with d = 2, 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.

Original languageEnglish
Pages (from-to)123-136
Number of pages14
JournalComputational Methods in Applied Mathematics
Volume19
Issue number1
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes

Keywords

  • B-Splines Isogeometric Matrix Assembly
  • Isogeometric Analysis
  • Low-Rank Approximation
  • Parabolic Initial-Boundary Value Problems

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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