 # The Geometry of the Model and the Problem Space

The major concern of every CEM model is the geometry of the problem to be solved. A less complex representation must be created, which includes all the important details while avoiding unnecessary details. In addition to the fixed portions of the geometry, it is often necessary to include variables such as the range of positions in which a nearby wire - or any other conductor - could be placed. Together with the geometry of a problem, the properties of all materials used must also be included in the model. If the computational domain were of infinite extent, the simulation of free space would be involved. This can be achieved by using mesh truncation techniques or absorbing boundary conditions. These techniques require that extra free space is added around the model components.

# Numerical Computation Methods

Substantial advancements have been made in enhancing the important numerical techniques - for example: the method of moments (MoM); the finite-difference time-domain (FDTD) method; the finite-element method (FEM); the proposed harmonic balance method (HBFEM) in this book; and the transmission line matrix (TLM) method. Many numerical methods were invented decades ago but, in all cases, additional novel ideas were required to make them applicable to today’s real-world electromagnetic problems.

• • The quasi-static field can be expressed by several different partial differential equations (PDEs). Although existing computational electromagnetic solvers provide preliminary insight, a multi-physics simulation system is needed to model coupled problems in their entity. Multi-physics problems are often related to more than two fields, such as thermal and E fields, or the H field, thermal dynamic field, and so forth. In the quasi-static field, the following methods are often used in FEM based EM computation:
• • Time-domain techniques use a band-limited impulse to excite the simulation across a wide frequency range. The result obtained from a time-domain code is the model’s response to this impulse. Where frequency-domain information is required, a Fourier transform is applied to the time-domain data.
• • Frequency-domain codes solve for one frequency at a time. This is usually adequate for antenna work or electric machine simulation, and for examining specific issues. Frequency-domain codes are, in general, faster than their time-domain cousins. Therefore, several frequency-domain simulations can usually be run in the time it would take for a single time-domain simulation. However, in nonlinear EM field problems, there is a coalition between each frequency domain, particularly for solving harmonic problems in nonlinear time periodic problems. This can be called the multi-frequency-domain or HBFEM. 