Efficient EM Topology Optimization Incorporating Advanced Matrix Padé Via Lanczos and Genetic Algorithm for Microwave Design

Electromagnetic (EM) topology optimization aims at finding the optimal shape and topology of the EM structure by adding or eliminating materials, such as metal within the design space. This optimization problem cannot be solved by the widely used surrogate-based optimization because different shapes and topologies cannot be related by changing the values of a given set of geometrical parameters. EM simulations are needed when the shape and topology change. This article proposes an efficient EM topology optimization technique for microwave component design. The finite element method (FEM) is used for EM simulation. We propose a new method to integrate the matrix Padé via Lanczos (MPVL) and the Householder formula. The proposed method combines the advantages of the MPVL and the Householder formula so that the effort of solving the large FEM matrix equation at many frequencies is reduced to the effort of solving only a small matrix problem at a single frequency point, thereby speeding up the topology optimization process. We further propose a new method to reduce the small matrix problem into an even smaller one by exploiting the inheritance pattern of a genetic algorithm (GA). New formulations are derived to exploit the common factors between new children EM structures and the parent EM structures in each generation of GA so that computational expense can be further reduced. The proposed technique incorporating advanced FEM-MPVL and the inheritance pattern of GA can greatly accelerate the topology optimization process. Three microwave examples are used to demonstrate the proposed technique.