微结构几何模型等几何矩阵的快速多尺度构造
Fast and Multiscale Formation of Isogeometric matrices of Microstructured Geometric Models
摘要：
高阶离散化的矩阵形成是已知的数值要求。基于现有的插值和查找过程，我们设计了一个多尺度的组装过程，以减少过高的组装时间的背景下，通过样条组合物建模的复杂微结构几何形状的等几何线弹性。所开发的等几何方法涉及发生在宏观尺度的多项式逼近和使用的查找表与预先计算的积分纳入微观尺度的信息。我们提供了理论见解和数值例子来研究该程序的性能。该策略被证明是非常感兴趣的，不仅形成有限元算子，而且以快速的方式计算其他量，例如通常用于设计优化的灵敏度分析。
英文摘要：
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.
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