Potential-based electromagnetic analysis: hybrid discrete exterior calculus and surface integral equation framework

Background. Analyzing electromagnetic fields in complex, multi-material environments is computationally demanding. Classical field-based integral equation formulations break down at low frequencies and become ill-conditioned for high-contrast materials, which limits their use for electrically large, heterogeneous industrial systems such as layered media and chip packages.

Objective. Develop a unified, efficient, and physically consistent solver for electromagnetic scattering and radiation in complex geometries and heterogeneous materials that is immune to low-frequency breakdown and naturally compatible with multiphysics coupling.

Approach. We couple discrete exterior calculus (DEC) with surface integral equations (SIE) in the potential-based (A–Φ) formulation of Maxwell’s equations under the Lorenz gauge. The inhomogeneous interior is discretized with DEC, a coordinate-free framework that preserves topological invariants on unstructured meshes, while the homogeneous exterior is treated with SIEs, which satisfy the radiation condition without artificial domain truncation. A scalar reformulation of the SIEs reduces the number of surface integral operators from fourteen to two by working with the Cartesian components of the vector potential and their normal derivatives; correspondingly, each vector potential component is represented as a discrete 0-form in the DEC domain.

Main results. The 0-form treatment improves compatibility at the DEC–SIE interface and significantly enhances numerical performance, yielding a hybrid method for scattering and radiation problems in heterogeneous media.

Significance and ongoing work. This framework is a building block for the scalable solvers we are developing with the Consortium for Electromagnetic Technologies for layered media, chip packaging, and lithography (see fast integral equation solvers for layered media and chip packaging).

Publications.

A. Abdrabou (PD) and L. J. Gomez, "A Hybrid DEC-SIE Framework for Potential-Based Electromagnetic Analysis of Heterogeneous Media," Journal of Computational Physics, vol. 553, pp. 114726, 2026. link