Stable Isogeometric Analysis of Trimmed Geometries

TL;DR

This paper introduces extended B-splines as a stable basis for isogeometric analysis on trimmed geometries, demonstrating their effectiveness in boundary element formulations for various problems.

Contribution

It presents a novel stabilization method using extended B-splines for isogeometric analysis with trimmed geometries, including construction for non-uniform knot vectors.

Findings

Excellent results in interpolation, potential, and linear elasticity problems.

Stable basis reduces ill-conditioning in trimmed geometries.

Flexible stabilization scheme suited for isogeometric analysis.

Abstract

We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.