EigenFunction Analysis with MultiLoop III
Eigenfunction analysis of thin sheet conductors was pioneered by Peter Annan in 1974. Eigenfuntions are sets of non-interacting basis functions, each of which have their own characteristic decay times governed in part by the size of the eigen values. Eigenfunctions can be computed in MultiLoop III. The larger eigenfunctions correspond to mathematical functions one would typically derive from a solution to Helmholtz' equation for a particular shape, while the smaller eigenfunctions (on the scale of mesh elements) tend to reflect the character of the mesh.
Eigen functions can be viewed in the movies below; the movie must load first, then it will play automatically.
For example, the larger eigenfunctions of a disk are similar to the cylindrical eigenfunctions that would be derived analytically from the Helmholtz equation.
For an annulus, the eigen function spectrum will be bifurcated into two parts. One set of eigenfunctions will have long decays; these eigen functions correspond to currents flowing around the hole in the annulus. The second set will have small decays, and correspond to current vortices that do not flow around the hole.