Methods in electromagnetism

Methods in electromagnetism are mathematical and computational techniques for formulating, solving, and analyzing problems involving electric and magnetic fields.

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Maxwell's equations: Four equations describing how electric and magnetic fields are produced and how they interact. They provide the governing relations that electromagnetic solution methods must satisfy.
Separation of variables: A technique that seeks solutions as products of functions, each depending on one coordinate. It solves many boundary-value problems when the geometry matches a suitable coordinate system.
Electrostatics: The study of electric fields and charges that do not vary with time. Scalar-potential methods and Poisson equations are central to static electric-field solutions.
Finite element method: A numerical method that approximates differential-equation solutions using piecewise functions on a mesh. Its flexible unstructured meshes contrast with the regular grids typical of finite-difference schemes.
Electromagnetic potential: Scalar and vector fields from which electric and magnetic fields can be derived. Potentials often simplify calculations and expose gauge freedom.
Multipole expansion: A representation of a field by successively higher-order source moments. It approximates distant fields using compact information about their sources.
Magnetostatics: The study of magnetic fields produced by steady currents and stationary magnetic materials. Vector potentials and magnetostatic boundary-value methods address steady-current systems.
Finite-difference time-domain method: A numerical technique that advances discretized electromagnetic fields through time and space. Its explicit time stepping contrasts with frequency-domain methods that solve one frequency at a time.
Boundary condition: A constraint specifying a solution's behavior at the boundary of a domain or interface. Field values and material interfaces determine which mathematical solution is physically admissible.
Method of moments: A numerical technique that converts integral equations into finite systems of weighted equations. It is widely used for radiation and scattering problems with surface or wire currents.