Sum-factorization techniques in Isogeometric Analysis

Abstract

The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order $p$. Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approach is applied to Gauss quadrature, the computational complexity grows as $p^{d+2}$ instead of $p^{2d+1}$ as previously achieved.

34 pages, 8 figures

References in corpus (3)

• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method

Cited by in corpus (6)

• Industrial scale large eddy simulations (LES) with adaptive octree meshes using immersogeometric analysis
• The surrogate matrix methodology: Low-cost assembly for isogeometric analysis
• Weighted quadrature for hierarchical B-splines
• The surrogate matrix methodology: Accelerating isogeometric analysis of waves
• Fast formation and assembly for spline-based 3D fictitious domain methods
• Fast formation and assembly of isogeometric Galerkin matrices for trimmed patches