Comparative study of different quadrature methods for cut elements

TL;DR

This paper reviews and benchmarks various open-source quadrature methods for cut elements in finite element analysis, evaluating their efficiency, accuracy, and robustness across 2D and 3D geometries.

Contribution

It provides a comprehensive comparison of existing open-source codes and develops benchmark examples to assess their performance in different scenarios.

Findings

Efficiency varies with input parameters

Accuracy depends on quadrature order

Robustness is tested across multiple geometries

Abstract

The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some available as open-source implementations. This work reviews these open-sources codes and the methods used. Furthermore, benchmarking examples are developed for 2D and 3D geometries. Implicit and explicit boundary descriptions are available for all models. The different examples test the efficiency, accuracy, versatility, and robustness of the codes. Special focus is set on the influence of the input parameter, which controls the desired quadrature order, on the actual integration error. A detailed comparison of the discussed codes is carried out. The benchmarking allows a conclusive comparison and presents a valuable tool for future code development. All tests are published in an accompanying open-source repository.