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.

翻译：切割单元的数值积分对所有不采用边界拟合网格的有限元方法都至关重要。该过程应具备高效性、精确性和鲁棒性。目前已发表多种平衡这些需求的方法，其中部分已提供开源实现。本研究系统评述了这些开源代码及其采用的方法。此外，针对二维和三维几何结构开发了基准测试案例集。所有模型均支持隐式和显式边界描述方式。通过不同算例测试了各代码的效率、精度、通用性和鲁棒性。研究特别关注控制目标求积阶数的输入参数对实际积分误差的影响机制。对讨论的代码进行了详细对比分析。基准测试体系实现了结论性比较，为未来代码开发提供了重要工具。所有测试案例均已发布于配套的开源代码库中。