Fields are nowadays often solved using numeric digital field simulation packages. The principal methods used are shown in Fig. 2.17.
Fig. 2.17: Principal methods of field simulation
In the finite difference method (FDM) and the finite element method (FEM), the relevant field
region is subdivided into a rectangular or triangular mesh, respectively. The potentials at the
node points are solved numerically, taking into account the boundary conditions. In the case
of the electrostatic field, this amounts to a numeric solution of La Place’s equation for the
In the case of the charge simulation method (CSM), fictitious charges are placed inside the
electrodes (outside the field region). For the boundary element method (BEM), surface
charge elements are placed on the electrode surface. The values of these fictitious charges
are computed, taking into account the boundary conditions. Thereafter, the fields can be
computed for any point, such as P(x,y,z) within the field region.
The field simulations in Figs. 2.7 to 2.12 were done using a boundary element package.