用于修剪面片的等几何伽辽金矩阵的快速构造与组装
Fast formation and assembly of isogeometric Galerkin matrices for trimmed patches
AI总结：
本研究针对修剪双变量参数空间的等几何伽辽金矩阵构造，提出混合高斯点法和不连续加权求积两种基函数处理方案，均实现显著加速，分别适配中、高基函数次数场景。
摘要：
本研究探讨了将文献[8,17]中的快速组装与构造策略应用于修剪双变量参数空间的方法。针对被修剪曲线截断的基函数，研究了两种处理思路：一种采用基于混合高斯点的方法，另一种则计算不连续加权求积规则。研究针对质量矩阵的构造及其在L2投影中的应用，检验了这两种思路的精度与效率。结果显示，与标准的逐单元有限元构造方式相比，该方法实现了显著的速度提升。两种提出的思路之间并无明确的优劣偏好：不连续加权方案的计算规模随基函数次数增长的表现更优，但需要额外投入计算求积权重的工作量；混合高斯方法则不存在这一开销，其开销由修剪曲线的复杂度决定。因此，混合高斯方法适用于中等次数的场景，而不连续加权求积方法在高次数场景下具有潜力，尤其是在相关权重可并行计算的情况下。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
