This article addresses the efficient numerical analysis of sparsely distributed small modifications in a large structure, that is, the sparsely distributed partial modification problem (SDPMP). A hierarchical matrix (H-matrix)-based fast direct solver is adopted to solve the SDPMP in a very short time for each new set of modifications. The main idea of this method is to reuse the parts of the compressed inverse matrix operator that do not change and only recompute the modified parts. In contrast with already existing algorithms designed to tackle a single localized modification, this new approach is still very fast for sparsely distributed small modifications, so it becomes a very attractive option to solve optimization problems efficiently, due to the very cheap analysis of the modified structure at each iteration of the optimization procedure. The efficiency of the solution of SDPMP is demonstrated for several cases involving passive and active metasurfaces and a reconfigurable antenna. As a practical example, a programmable metasurface reflector is optimized with particle swarm optimization to obtain a prescribed reflection pattern.

中文翻译：

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稀疏分布偏修正问题的快速分析与优化

本文解决了大型结构中稀疏分布的小修改的有效数值分析，即稀疏分布的部分修改问题（SDPMP）。采用基于分层矩阵（H-matrix）的快速直接求解器在很短的时间内对每组新的修改求解 SDPMP。该方法的主要思想是重用压缩逆矩阵算子中不变的部分，只重新计算修改后的部分。与旨在解决单个局部修改的现有算法相比，这种新方法对于稀疏分布的小修改仍然非常快，因此它成为有效解决优化问题的非常有吸引力的选择，因为修改后的结构分析非常便宜在优化过程的每次迭代中。SDPMP 解决方案的效率在涉及无源和有源超表面和可重构天线的几种情况下得到证明。作为一个实际示例，可编程超表面反射器通过粒子群优化进行优化，以获得规定的反射模式。