Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a regular background mesh cut by a boundary representation that defines the domain of interest. Therefore, we present a novel concept to divide the support of cut basis functions to obtain regular parts suited for sum factorization. These regions require special discontinuous weighted quadrature rules, while Gauss-like quadrature rules integrate the remaining support. Two linear elasticity benchmark problems confirm the derived estimate for the computational costs of the different integration routines and their combination. Although the presence of cut elements reduces the speed-up, its contribution to the overall computation time declines with h-refinement.

翻译：结合求和分解、加权求积与逐行组装，可实现张量积样条的高效高阶计算。本文旨在将这些概念迁移至浸没边界法——该方法在由边界表示切割的规则背景网格上执行模拟，该边界表示定义了目标区域。为此，我们提出一种创新概念：通过分割切割基函数的支撑域，得到适用于求和分解的规则子区域。这些区域需采用特殊的不连续加权求积规则，而剩余支撑域则沿用高斯型求积规则。两个线弹性基准问题验证了不同积分程序及其组合计算成本的推导估算。尽管切割单元的存在会降低加速比，但其对整体计算时间的贡献会随h加密而递减。