Math 2.0

Partial differential equations Definition

Computational electromagnetics

Builds on Maxwell's equationsConstitutive relations of electromagnetismSilver–Müller radiation condition

Definition

An electromagnetic field problem consists of these data:

  1. a region of space, possibly unbounded, with the constitutive relations of the materials in it;
  2. given sources, such as currents or incident fields;
  3. boundary conditions, and for unbounded regions a radiation condition such as the Silver–Müller condition.

Its solution is the field that satisfies Maxwell's equations with these data, in the time domain or at a fixed frequency. Computational electromagnetics is the study and use of methods that approximate this solution by the solution of a finite system of algebraic equations. Such a method consists of a discretization, which replaces the fields by finitely many unknowns, and an algorithm that solves the resulting system.

Remarks

Example: the finite-difference time-domain method satisfies the definition. Its unknowns are field values on a grid, and its algebraic equations are the difference equations that update them step by step in time.

Non-example: the Mie series gives the field scattered by a homogeneous sphere as an explicit infinite sum. It is an exact formula, not a discretization of the problem, so it is not itself a method of computational electromagnetics, though it is used to test such methods.

The methods are usually sorted in two ways: time domain or frequency domain, and differential equation on a volume or integral equation on a surface.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Constitutive relations of electromagnetism, concept, no evidence levelConstitutive relation…conceptMaxwell's equations, concept, no evidence levelMaxwell's equationsconceptSilver–Müller radiation condition, concept, no evidence levelSilver–Müller radiati…conceptComputational electromagnetics, definition, no evidence levelComputational electro…definition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Constitutive relations of electromagnetism concept
  2. Maxwell's equations concept
  3. Silver–Müller radiation condition concept
  4. Computational electromagnetics definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Computational_electromagnetics
About this page
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MSC35Q61, 65Z05, 78A25
DefinesComputational electromagnetics
UsesMaxwell's equations, Constitutive relations of electromagnetism, Silver–Müller radiation condition
Changed3 November 2026

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