This work explores the application of the fast assembly and formation strategy from [8, 17] to trimmed bi-variate parameter spaces. Two concepts for the treatment of basis functions cut by the trimming curve are investigated: one employs a hybrid Gauss-point-based approach, and the other computes discontinuous weighted quadrature rules. The concepts' accuracy and efficiency are examined for the formation of mass matrices and their application to L2-projection. Significant speed-ups compared to standard element by element finite element formation are observed. There is no clear preference between the concepts proposed. While the discontinuous weighted scheme scales favorably with the degree of the basis, it also requires additional effort for computing the quadrature weights. The hybrid Gauss approach does not have this overhead, which is determined by the complexity of the trimming curve. Hence, it is well-suited for moderate degrees, whereas discontinuous-weightedquadrature has potential for high degrees, in particular, if the related weights are computed in parallel.

翻译：这项工作探索了快速组装和编组战略从[8, 17]到减缩双变量参数空间的应用。调查了处理由三角曲线切割的基函数的两个概念:一个采用混合高斯点法,另一个计算不连续加权二次曲线规则。为形成质量矩阵和将其应用于L2-project,对概念的准确性和效率进行了检查。观察到了与标准要素有限要素形成的标准元素相比的快速增速。在所提出的概念之间没有明显的偏好。虽然不连续加权比例比重优于基数,但也要求作出额外的努力来计算二次曲线的重量。混合高标法没有这一由三重曲线复杂性决定的顶部。因此,它非常适合中等度,而不连续加权的夸德具有很高的潜能,特别是如果相关的重量是平行计算的话。