The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly time in the context of isogeometric linear elasticity of complex microstructured geometries modeled via spline compositions. The developed isogeometric approach involves a polynomial approximation occurring at the macro-scale and the use of lookup tables with pre-computed integrals incorporating the micro-scale information. We provide theoretical insights and numerical examples to investigate the performance of the procedure. The strategy turns out to be of great interest not only to form finite element operators but also to compute other quantities in a fast manner as for instance sensitivity analyses commonly used in design optimization.

中文翻译：

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微结构几何模型等几何矩阵的快速多尺度形成

众所周知，与高阶离散化相关的矩阵形成对数值要求很高。基于现有的插值和查找程序，我们设计了一个多尺度组装程序，以减少在通过样条组合建模的复杂微结构几何的等几何线性弹性背景下过多的组装时间。开发的等几何方法涉及在宏观尺度上发生的多项式近似，以及使用包含微观尺度信息的预计算积分的查找表。我们提供理论见解和数值示例来研究程序的性能。