A study of disparate grid sizes for an irregular-shape scatterer on EFIE, MFIE, and CFIE

We have implemented a numerical algorithm for solving the integral equations of electromagnetic scattering from conducting objects using the method of moments. This code is implemented and developed for the computation of near-field interactions in the multilevel fast multipole algorithm (MLFMA). The implementation utilized the flat-triangular patch for the surface description and the Rao-Wilton-Glisson (1982) basis as the current expansion function. The triangular patch basis was introduced by Rao et. al. for solving the electrical field integral equation (EFIE). Our implementation is focused on the consideration of reducing the condition number of the impedance matrix. Hence, the implementation includes the electrical field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE). In the computation of the matrix elements associated with the nearby elements, the near-singular integrals are treated properly with the aid of the formulas given previously. This allows the code to deal with objects that contain very thin structures. Moreover, we added a partial diagonal preconditioner in the code in case the iterative solver does not provide any preconditioners. This is very important in the Galerkin´s method. We have tested the code for various ill-conditioning problems to validate the performance of the implementation.