Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

Low Rank Tensor Methods in Galerkin-based Isogeometric Analysis

Abstract : The global (patch-wise) geometry map, which describes the computational domain, is a new feature in isogeometric analysis. This map has a global tensor structure, inherited from the parametric spline geometry representation. The use of this global structure in the discretization of partial differential equations may be regarded as a drawback at first glance, as opposed to the purely local nature of (high-order) classical finite elements. In this work we demonstrate that it is possible to exploit the regularity of this structure and to identify the great potential for the efficient implementation of isogeometric discretizations. First, we formulate tensor-product B-spline bases as well as the corresponding mass and stiffness matrices as tensors in order to reveal their intrinsic structure. Second, we derive an algorithm for the the separation of variables in the integrands arising in the discretization. This is possible by means of low rank approximation of the integral kernels. We arrive at a compact, separated representation of the integrals. The separated form implies an expression of Galerkin matrices as Kronecker products of matrix factors with small dimensions. This representation is very appealing, due to the reduction in both memory consumption and computation times. Our benchmarks, performed using the C++ library G+Smo, demonstrate that the use of tensor methods in isogeometric analysis possesses significant advantages.
Complete list of metadata

Cited literature [60 references]  Display  Hide  Download
Contributor : Angelos Mantzaflaris Connect in order to contact the contributor
Submitted on : Tuesday, August 27, 2019 - 11:55:51 AM
Last modification on : Friday, February 4, 2022 - 3:19:54 AM


Files produced by the author(s)




Angelos Mantzaflaris, Bert Jüttler, Boris Khoromskij, Ulrich Langer. Low Rank Tensor Methods in Galerkin-based Isogeometric Analysis. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 316, pp.1062-1085. ⟨10.1016/j.cma.2016.11.013⟩. ⟨hal-02271847⟩



Record views


Files downloads