An elementary formula for computing shape derivatives of EFIE system matrix

TL;DR

This paper derives an analytical formula for computing shape derivatives of the EFIE system matrix, enabling efficient and accurate sensitivity analysis in electromagnetic simulations.

Contribution

It introduces a new analytical approach for shape derivatives of EFIE matrices, validated against automatic differentiation and finite differences.

Findings

Analytical derivatives match numerical methods closely

Method simplifies computation of shape sensitivities

Applicable to discretizations with Raviart-Thomas basis functions

Abstract

We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in excellent agreement.