Numerical Methods in Electromagnetic Fields

Numerical solution of electromagnetic field problems arise in high frequency - light current and low frequency - heavy current situations. Such problems are governed by Maxwell field equations in differential and integral form and their solution is dependent upon ht geometry, properties of the medium, and the boundary and initial conditions. Elliptic partial differential equations, such as the Laplace, poisson and Helmholtz equations, are associated with steady state phenomena, i.e., boundary value problems usually modeling closed or bounded solution regions. Parabolic equations are generally associated with problems of diffusion as electromagnetic field penetration and related effects of eddy current phenomena. Hyperbolic equations arise in propagation problems, an example being the electromagnetic wave equation. The solution region is usually open so that a solution advances outwards indefinitely from initial conditions while always satisfying specified boundary conditions. Access to high speed computers and numerical methods has enabled us to solve many complex electromagnetic problems faster and at less cost. Of even greater significance is the fact that the approach enables us to undertake problems that could never have been attempted without them.