Partial tensor decomposition for decoupling isogeometric Galerkin discretizations

Felix Scholz, Angelos Mantzaflaris, Bert Jüttler

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

System matrix assembly for isogeometric (i.e., spline-based) discretizations of partial differential equations is more challenging than for classical finite elements, due to the increased polynomial degrees and the larger (and hence more overlapping) supports of the basis functions. The global tensor-product structure of the discrete spaces employed in isogeometric analysis can be exploited to accelerate the computations, using sum factorization, precomputed look-up tables, and tensor decomposition. We generalize the third approach by considering partial tensor decompositions. We show that the resulting new method preserves the global discretization error and that its computational complexity compares favorably to the existing approaches. Moreover, the numerical realization simplifies considerably since it relies on standard techniques from numerical linear algebra.

Original languageEnglish
Pages (from-to)485-506
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume336
DOIs
Publication statusPublished - 2018 Jul 1
Externally publishedYes

Keywords

  • Isogeometric analysis
  • Low-rank approximation
  • Matrix assembly
  • Numerical integration
  • Singular value decomposition
  • Tensor decomposition

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Partial tensor decomposition for decoupling isogeometric Galerkin discretizations'. Together they form a unique fingerprint.

Cite this