Accurate and efficient solutions of electromagnetic problems with the multilevel fast multipole algorithm

The multilevel fast multipole algorithm (MLFMA) is a powerful method for the fast and efficient solution of electromagnetics problems discretized with large numbers of unknowns. This method reduces the complexity of matrix-vector multiplications required by iterative solvers and enables the solution of largescale problems that cannot be investigated by using traditional methods. On the other hand, efficiency and accuracy of solutions via MLFMA depend on many parameters, such as the integral-equation formulation, discretization, iterative solver, preconditioning, computing platform, parallelization, and many other details of the numerical implementation. This dissertation is based on our efforts to develop sophisticated implementations of MLFMA for the solution of real-life scattering and radiation problems involving three-dimensional complicated objects with arbitrary geometries.