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Differential Form of Maxwell's Equations

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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.

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Updated: May 19, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Non-conformal domain decomposition methods for time-harmonic Maxwell equations.

Yang Shao¹, Zhen Peng, Kheng Hwee Lim

¹ElectroScience Laboratory, Department of Electric and Computer Engineering , Ohio State University , Columbus, OH 43212, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences

|August 8, 2012

Summary

This summary is machine-generated.

This review explores non-conformal domain decomposition methods (DDMs) for complex electromagnetic (EM) problems. These advanced techniques, including finite-element and integral equation approaches, efficiently solve large-scale radiation and scattering challenges.

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Area of Science:

Computational Electromagnetics
Numerical Analysis

Background:

Electrically large and multi-scale electromagnetic (EM) radiation and scattering problems pose significant computational challenges.
Existing domain decomposition methods (DDMs) often struggle with the complexity and scale of these EM problems.

Purpose of the Study:

To review non-conformal domain decomposition methods (DDMs) for solving electrically large and multi-scale EM radiation and scattering problems.
To detail the formulation and application of a specific finite-element DDM (FETI-like) and its extension to integral equation methods.

Main Methods:

Detailed discussion of a finite-element DDM incorporating Robin transmission conditions and an edge corner penalty term.
Extension of non-conformal DDM to surface integral equation methods, including non-conformal integral equation DDM and a generalized combined field integral equation method.
Application of a multi-solver DDM for simulating plane wave scattering from a composite mockup fighter jet.

Main Results:

The reviewed non-conformal DDMs demonstrate efficacy in handling complex EM radiation and scattering scenarios.
The finite-element DDM with FETI-like algorithm and specific boundary conditions is effective for problems with repetitions.
Integral equation based non-conformal DDMs provide viable modeling for scattering from various targets.

Conclusions:

Non-conformal DDMs offer a powerful framework for addressing computationally intensive EM problems.
The presented methods, including finite-element and integral equation approaches, show promise for future advancements in EM simulations.
Successful simulation of a complex scenario (fighter jet scattering) validates the utility of the developed multi-solver DDM.