Representing a Field Quantity in the Method of Moments (MoM)

Using MoM, field quantities are interpolated over elements, but typically with simpler basis functions than in Finite Element Method (FEM).

For capacitance problems, the field quantity of interest is the charge density on the surface of a conductor or dielectric interface. Triangular elements are used, and the charge density is approximated with a piecewise-constant basis function.

For inductance problems, the field quantity is a vector (current density), and again piecewise-constant basis functions are used. For DC inductance problems, the elements are tetrahedra (volume currents), and for AC inductance problems the elements are triangles (surface currents).

MoM differs significantly from FEM in the way that Maxwell 's equations are transformed into a matrix equation. A mathematical device called a Green 's function is used to represent the electrical interaction between any pair of elements. Using integrals of the Green 's function and the basis functions, a dense matrix of linear equations ("dense" because there are few or no zero-valued entries) is derived. A straightforward direct solution of such a dense matrix is prohibitively expensive, and so Q3D uses iterative matrix solvers and the Fast Multipole Method to make it practical to solve large problems.