Fast Convergence of Fast Multipole Acceleration Using Dual Basis Function in the Method of Moments for Composite Structures

The dual basis function proposed by Chen and Wilton in 1990 is used to represent the magnetic current for solving electromagnetic (EM) surface integral equations (SIEs) with penetrable materials and the solution process is accelerated with multilevel fast multipole algorithm (MLFMA) for large problems. The MLFMA is a robust accelerator for matrix equation solvers by iterative method, but its convergence rate strongly relies on the conditioning of system matrix. If the MLFMA is based on the method of moments (MoM) matrix in which the electric current is represented with the Rao-Wilton-Glisson (RWG) basis function, then how one represents the magnetic current in electric field integral equation (EFIE) and magnetic field integral equation (MFIE) really matters for the conditioning of system matrix. Though complicated in implementation, the dual basis function is ideal to represent the magnetic current because it is similar to the RWG basis function in properties but approximately orthogonal to it in space. With a simple testing scheme, the resultant system matrix is well-conditioned and the MLFMA acceleration can be rapidly convergent. Numerical examples for EM scattering by large composite objects are presented to demonstrate the robustness of the scheme.