Small Variable Matrix Extraction Techniques for Accelerating the Electromagnetic Topology Optimization

Electromagnetic topology optimization has become an essential technique for the automatic design of high-performance microwave and radio-frequency components. However, the repeated solution of large-scale electromagnetic problems across multiple topologies and frequency points poses significant computational challenges. This paper reviews three representative fast topology optimization methods—Householder formula-based fast frequency sweep, design space decomposition, and lower and upper triangular matrices reconstruction-based fast frequency sweep—which aim to accelerate the evaluation of electromagnetic responses. Each method extracts one or several small variable matrices that can be efficiently updated and solved, thereby reducing the cost of solving full-scale system equations. The Householder-based method excels in scenarios with a small number of design sub-spaces; the design space decomposition method is more suitable for problems with multiple design sub-spaces but few frequency samples; and the lower and upper triangular matrices reconstruction-based method is designed for multiple design sub-spaces, broadband optimization tasks, offering efficient frequency sweeping with modest memory usage. The comparative analysis in this review highlights the strengths and applicable scenarios of each method, offering guidance for selecting the most appropriate acceleration strategy in electromagnetic topology optimization.