Comparison of Integration Methods for Cut Elements

TL;DR

This paper compares integration methods for cut elements defined by implicit and parametric curves, evaluating their efficiency and robustness in geometric and elasticity problems using open-source tools.

Contribution

It provides a comparative analysis of implicit and parametric interface descriptions for cut element integration, highlighting that the choice depends on the problem and curve description.

Findings

No clear superiority in integration quality between the two interface types.

Choice of interface depends on problem specifics and available curve description.

Both methods are viable depending on the application context.

Abstract

Using an interface inserted in a background mesh is an alternative way of constructing a complex geometrical shape with a relative low meshing efforts. However, this process may require special treatment of elements cut by the interface. Our study focuses on comparing the integration of cut elements defined by implicit and parametric curves. We investigate the efficiency and robustness of open-source tools such as Algoim [5](a library for quadrature on implicitly defined geometries) and Ginkgo [2](a library for isogeometric analysis on Boolean operations with a parametric description) with numerical examples computing the area defined by the interface and benchmarks for 2D elasticity problem using the open-source code GeoPDEs [7]. It is concluded that none of the two interface descriptions is preferable with respect to the quality of the integration. Thus, the choice of the interface type depends only on the studied problem and the available curve description, but not on the numerical aspects of the integration.