An improvement of the finite-element method for computing the electric field of waveguides with complex geometry

Curvilinear elements have been reported to be one of the more advantageous features of the finite-element method (FEM), since they allow fitting arbitrarily shaped geometries without staircase approximations, thus leading to more accurate results. Nevertheless, the graphical representation of the computed fields involves quite complex computations. In this paper, the homotopy continuation method has been specialized for solving the systems of polynomial equations arising when the electromagnetic field obtained through the FEM is computed at an arbitrary point within the solution domain. The results obtained with this method are satisfactorily compared with those provided by other classical widely used procedures, like the Newton's method.