Fast immersed boundary method based on weighted quadrature

Abstract

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a regular background mesh cut by a boundary representation that defines the domain of interest. Therefore, we present a novel concept to divide the support of cut basis functions to obtain regular parts suited for sum factorization. These regions require special discontinuous weighted quadrature rules, while Gauss-like quadrature rules integrate the remaining support. Two linear elasticity benchmark problems confirm the derived estimate for the computational costs of the different integration routines and their combination. Although the presence of cut elements reduces the speed-up, its contribution to the overall computation time declines with h-refinement.

References in corpus (9)

• High order unfitted finite element methods on level set domains using isoparametric mappings
• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
• Isogeometric Analysis on V-reps: first results
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
• A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems
• Patch-wise Quadrature of Trimmed Surfaces in Isogeometric Analysis
• Weighted quadrature for hierarchical B-splines
• Fast formation and assembly for spline-based 3D fictitious domain methods