Stable Isogeometric Analysis of Trimmed Geometries

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.

References in corpus (2)

• Fast Isogeometric Boundary Element Method based on Independent Field Approximation
• A simple approach to the numerical simulation with trimmed CAD surfaces

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• A CFL condition for the finite cell method
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• A Consistent Higher-Order Isogeometric Shell Formulation
• Immersed Boundary-Conformal Isogeometric Method for Linear Elliptic Problems
• Advances in the Treatment of Trimmed CAD Models due to Isogeometric Analysis
• Generalized eigenvalue stabilization for immersed explicit dynamics