FINITE-ELEMENT COMPUTATION OF ELECTROMAGNETIC-FIELDS

A three dimensional finite element solution scheme is developed for nu merically computing electromagnetically induced power depositions. The solution method is applicable to those problems for which it can be r easonably assumed that the magnetic permeability is homogeneous. The m ethod employs an incident field/scattered field approach where the inc ident field is precalculated and used as the forcing function for the computation of the scattered field. A physically logical condition is used for the numerical boundary conditions to overcome the fact that e lectromagnetic problems are generally unbounded (i.e., the boundary co ndition is applied at infinity) but numerical models must have a bound ary condition applied to some finite location. At that numerical bound ary, an outgoing spherical wave is simulated. Finally, an alternate to a direct solution scheme is described. This alternate method, a preco nditioned conjugate gradient solver, provides both a storage and CPU t ime advantage over direct solution methods. For example, a one-thousan d fold decrease in CPU time was achieved for simple test cases. Unlike most iterative methods, the preconditioned conjugate gradient techniq ue used has the important property of guaranteed convergence. Solution s obtained from this finite element method are compared to analytic so lutions demonstrating that the solution method is second-order accurat e.