A Novel Design Space Decomposition Technique to Accelerate FEM-Based Electromagnetic Topology Optimization for Waveguide Structures

In radio frequency (RF) and microwave design optimization, electromagnetic (EM) simulation is crucial yet time-consuming. Solving extensive system equations is computationally expensive for finite-element method (FEM)-based EM simulation. In addition, during optimization, changes to the EM structure are often incremental, leading to inefficiencies in generating and solving new FEM system equations. To address this situation, this article proposes a novel design space decomposition (DSD) technique to rapidly calculate the EM response ( $S$ -parameter) of EM waveguide structures featuring newly optimized topologies. The proposed DSD technique is to segment the variable in the whole design space into several small variables in subspaces. Specifically, the FEM system matrix is decomposed into a constant part and a variable part, where the variable part can be further decomposed into a diagonal block matrix. Subsequently, a novel algorithm is developed to expedite the calculation of the EM response when modifications are applied to the diagonal block matrix within the variable part. With the proposed algorithm, the size of the small matrix remains independent of the number of subspaces, maintaining its smallest size consistently. This streamlined approach facilitates rapid calculations. The proposed technique negates the need to compute the entire, extensive system matrix, thereby greatly reducing the computational burden. Consequently, the proposed technique expedites the overall EM topology optimization. The efficiency of the proposed method is demonstrated through two microwave examples.