Optimization of the electromagnetic scattering problem based on the topological derivative method.
Optimization of the electromagnetic scattering problem based on the topological derivative method.
复制标题
基于拓扑导数方法的电磁散射问题优化。
作者：
Julián L. Pita Ruiz;A. A. S. Amad;L. Gabrielli;A. Novotny
针对电磁设计问题，提出了一种基于拓扑导数概念的新优化方法。本质上，拓扑导数方法的目的是测量给定形状泛函对于奇异域扰动的敏感性，因此它在图像处理的形状和拓扑优化、反问题和超材料设计等许多相关领域都有应用。针对电磁散射问题严格推导拓扑导数，并将其用作梯度下降方向，以寻找电磁器件设计的局部最优。我们证明所得到的拓扑设计算法非常简单和高效，并且自然地导致二元设计，同时仅依赖于传统的电动力学有限元公式的解。最后，提出了几个在两个和三个空间维度上的数值实验来说明所提出的公式的性能。
A new optimization method based on the topological derivative concept is developed for the electromagnetic design problem. Essentially, the purpose of the topological derivative method is to measure the sensitivity of a given shape functional with respect to a singular domain perturbation, so that it has applications in many relevant fields such as shape and topology optimization for imaging processing, inverse problems, and design of metamaterials. The topological derivative is rigorously derived for the electromagnetic scattering problem and used as gradient descent direction to find local optima for the design of electromagnetic devices. We demonstrate that the resulting topology design algorithm is remarkably simple and efficient and naturally leads to binary designs, while depending only on the solution of the conventional finite element formulation for electrodynamics. Finally, several numerical experiments in two and three spatial dimensions are presented to illustrate the performance of the proposed formulation.