Isogeometric Boundary Element Method with Hierarchical Matrices

TL;DR

This paper introduces an efficient isogeometric boundary element method using hierarchical matrices and NURBS-based surface bisection, demonstrating its effectiveness in linear elasticity problems.

Contribution

It presents a novel collocation scheme with hierarchical matrices and a geometric bisection strategy for NURBS surfaces in isogeometric boundary element methods.

Findings

Numerical results confirm the method's accuracy and efficiency.

The approach effectively handles mixed boundary value problems.

Hierarchical matrices improve computational performance.

Abstract

In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value problems, a block system of matrices similar to Galerkin formulations is constructed allowing an effective application of that matrix format. We introduce a strategy for the geometric bisection of surfaces based on NURBS patches. The approximation of system matrices is carried out by means of kernel interpolation. Numerical results are shown that prove the success of the formulation.