Numerical integration on trimmed three-dimensional domains with implicitly defined trimming surfaces

Abstract

We present a novel technique for the numerical integration of trivariate functions on trimmed domains. In our setting, we assume that the trimming surface is defined implicitly. Our approach combines a linear approximation of the trimming surface with a correction term. The latter term makes it possible to achieve a cubic convergence rate, which is one order higher than the rate obtained by using the linear approximation only. We also present numerical experiments that demonstrate the method’s potential for applications in isogeometric analysis.