Solver Selections Required For Solving High-Frequency Electromagnetic Field Problems

The method of moments (MoM) or the finite element method (FEM) can be used to solve electromagnetic field (EMF) problems. For open region problems like antennas, the use of MoM is more appropriate, whereas FEM is adequate for closed region problems like microwave cavities and networks. A team of engineering and software professionals designed the software program SINGULA to help solve a wide variety of high-frequency EMF problems. In the program the user has the option to choose the solver type depending up on the nature of the problem. A generalized hybrid method, that combines the MoM with the physical optics (PO) technique and the fast Fourier transform (FFT) method to speed up the matrix-vector multiplication, are implemented. This enables the solution of electrically large models. In this article, the formulations of these different methods along with an appropriate example for each of the method are presented. Where possible, the computed results are compared with those of published papers or the measured results reported in the literature.

Formulation Of BEM

The boundary element method (BEM) is based on integral equation formulation [1]-[4]. In high-frequency electromagnetic field applications, the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are the two widely used boundary integral equations. In the integral equation formulation the equivalent sources viz. the equivalent electric current density and the equivalent magnetic current density, which would sustain the field, are found by forcing them to satisfy prescribed boundary conditions under a function which relates the location and effect of the sources to any point on the boundary. This function, called the Green or influence function, effectively eliminates the need of a finite element mesh or a finite difference grid in the entire region of the problem provided the materials are linear.