Design Space Decomposition Algorithm for EM Topology Optimization of Multi-Iris Structures

Efficient electromagnetic (EM) topology optimization is often constrained by the computational cost of solving large system equations. This paper presents a finite element method (FEM)-based design space decomposition (DSD) algorithm to accelerate topology optimization for multi-iris structures. The DSD efficiently updates EM responses by applying the inverse formulas of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 \times 2$</tex> block matrices recursively, reducing the computational cost of solving a large sparse matrix to several smaller dense matrices. The number of smaller matrices scales linearly with the number of irises, while their dimensions remain constant, significantly speeding up multi-iris structure optimization. A three-pole waveguide filter is optimized as an example to demonstrate the efficiency of the DSD.