Partial tensor decomposition for decoupling isogeometric Galerkin discretizations

Felix Scholz (1) , Angelos Mantzaflaris (2, 3, 1) , Bert Jüttler (1, 4)

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

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.

Mots clés: isogeometric analysis; tensor decomposition; numerical integration; low-rank approximation; matrix assembly; singular value decomposition

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

Felix Scholz, Angelos Mantzaflaris, Bert Jüttler. Partial tensor decomposition for decoupling isogeometric Galerkin discretizations. Computer Methods in Applied Mechanics and Engineering, 2018, 336, pp.485-506. ⟨10.1016/j.cma.2018.03.026⟩. ⟨hal-02271800⟩