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.

中文翻译：

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快速形成和组装用于修整斑块的等几何Galerkin矩阵

这项工作探索了[8，17]中快速组装和形成策略在修剪后的双变量参数空间中的应用。研究了两种处理由修整曲线切出的基函数的概念：一种采用基于混合高斯点的方法，另一种计算不连续的加权正交规则。对质量矩阵的形成及其在L2投影中的应用，检查了概念的准确性和效率。与标准的逐元素有限元素形成相比，可以观察到明显的加速。提议的概念之间没有明确的偏爱。尽管不连续加权方案随基础程度有利地缩放，但它还需要额外的精力来计算正交权重。混合高斯方法没有这种开销，这取决于修整曲线的复杂程度。因此，它非常适合中等度数，而非连续加权正交具有高度数的潜力，特别是如果相关权重是并行计算的。