Fast Isogeometric Boundary Element Method based on Independent Field Approximation

TL;DR

This paper introduces a flexible, efficient isogeometric boundary element method for elasticity problems that independently approximates geometry, traction, and displacement, enabling advanced refinement and reduced computational costs.

Contribution

It presents a novel independent field approximation approach that enhances flexibility, efficiency, and accuracy in isogeometric boundary element analysis for elasticity.

Findings

Achieves optimal convergence rates in numerical studies.

Reduces computational complexity with hierarchical matrices.

Demonstrates effectiveness on real-world 2D and 3D examples.

Abstract

An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.