Rapid general electromagnetic analysis of metallic surfaces via conformal energy minimization

We recently found that the electromagnetic scattering problem can be solved efficiently using an approach that expresses the fields in terms of a set 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 planar metallic surfaces. The CEM algorithm enables 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 planar metallic surfaces: a square plate and a four-petal plate with semicircular side features. Our method extracts the circuit parameters, resonance frequencies, and resonance field distributions within seconds, accelerating resonant frequency determination by three orders of magnitude over conventional finite-element methods (e.g., COMSOL). Moreover, it directly and efficiently reveals low-energy, doubly degenerate resonance modes. These findings provide an analytical approach for calculating electromagnetic fields on complex geometries, contributing to the development of high-performance electromagnetic devices.