Rapid general Electromagnetic Analysis with computational conformal geometry via Conformal Energy Minimization

TL;DR

This paper introduces a fast electromagnetic analysis method using conformal geometry and energy minimization, transforming complex surfaces into a disk for simplified analysis, achieving significant efficiency gains over traditional methods.

Contribution

The paper presents a novel conformal energy minimization algorithm that enables rapid electromagnetic analysis on arbitrarily shaped metallic surfaces, outperforming traditional finite element methods.

Findings

Achieves three orders of magnitude faster computation than traditional methods

Successfully identifies resonance modes on complex geometries

Enables analysis of low-energy, doubly degenerate resonances

Abstract

We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply computational conformal geometry with the conformal energy minimization (CEM) algorithm to make possible fast solution of finite-frequency electromagnetic problems involving arbitrarily shaped, simply-connected metallic surfaces. The CEM algorithm computes conformal maps with minimal angular distortion, enabling the transformation of arbitrary simply-connected surfaces into a disk, where orthogonal basis functions can be defined and electromagnetic analysis can be significantly simplified. We demonstrate the effectiveness and efficiency of our method by investigating the resonance characteristics of two metallic surfaces: a square plate and a four-petal plate. Compared to traditional finite element methods (e.g., COMSOL), our approach achieves a three-order-of-magnitude improvement in computational efficiency, requiring only seconds to extract resonant frequencies and fields. Moreover, it reveals low-energy, doubly degenerate resonance modes that are elusive to conventional methods. These findings not only provide a powerful tool for analyzing electromagnetic fields on complex geometries but also pave the way for the design of high-performance electromagnetic devices.