Finite element modeling of open boundary problems

The authors explain how to compute open boundary problems in electromagnetism with good accuracy in the cases of two- and three-dimensional problems with existing classical finite-element method software. The proposed method is based on the use of an implicit spatial transformation to map the infinite exterior onto a finite domain; it requires very few modifications of code and is easy to implement in finite-element software. Comparisons with other methods show that the results are very good and that computer times are very competitive in relation to those of classical methods. Examples are given for 2-D Cartesian, 2-D axisymmetric, and 3-D problems. An advantage of the proposed method is that the matrix of the system to be solved is sparse and keeps a band structure, as in a classical finite-element problem