CutIGA with Basis Function Removal

TL;DR

This paper introduces a stabilized cut isogeometric method that removes basis functions with small domain intersection to maintain convergence, leveraging B-spline regularity for improved bounds.

Contribution

It proposes a novel basis function removal technique in cutIGA that preserves convergence rates and utilizes B-spline regularity for enhanced stability.

Findings

Convergence order remains unaffected by basis removal.

Basis function removal criteria depend on intersection size.

B-spline basis functions offer improved stability bounds.

Abstract

We consider a cut isogeometric method, where the boundary of the domain is allowed to cut through the background mesh in an arbitrary fashion for a second order elliptic model problem. In order to stabilize the method on the cut boundary we remove basis functions which have small intersection with the computational domain. We determine criteria on the intersection which guarantee that the order of convergence in the energy norm is not affected by the removal. The higher order regularity of the B-spline basis functions leads to improved bounds compared to standard Lagrange elements.