The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media

An efficient and accurate finite-element method is presented for computing transient electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both edge and Cartesian elements are used for approximating the spatial distribution of the field. The efficiency and the storage requirements of the method are further optimized by choosing an irreducible implicit formulation, by solving the resulting system of algebraic equations in terms of the time-dependent expansion coefficients iteratively, and by using an incomplete LU-decomposition for preconditioning. A method is described for imposing the divergence condition in a weighted sense. The theory discussed was implemented in the FEMAXT code