Shape Synthesis Based on Topology Sensitivity

TL;DR

This paper introduces a fast, impedance matrix inversion-free method for topology sensitivity analysis in electromagnetic shape synthesis, enabling real-time shape modification and optimization.

Contribution

It presents a novel topology sensitivity evaluation technique using basis functions, significantly faster than existing methods, suitable for real-time shape optimization.

Findings

Approximately 100 times faster than current approaches

Validates effectiveness through multiple examples

Can be integrated into EM simulation tools for topology optimization

Abstract

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique, provide important advantages, one of them being impedance matrix inversion free evaluation of the sensitivity. The devised procedure utilizes port modes and their superposition which, together with only a single evaluation of all matrix operators, leads to a computationally effective procedure. The proposed method is approximately one hundred times faster than contemporary approaches, which allows the investigation of the sensitivity and the modification of shapes in real-time. The method is compared with known approaches and its validity and effectiveness is verified using a series of examples. The procedure can be implemented in up-to-date EM simulators in a straightforward manner. It is shown that the iterative repetition of the topology sensitivity evaluation can be used for gradient-based topology synthesis. This technique can also be employed as a local step in global optimizers.