Large-scale solutions of electromagnetics problems using the multilevel fast multipole algorithm and physical optics

Integral equations provide full-wave (accurate) solutions of Helmholtz-type electromagnetics problems. The multilevel fast multipole algorithm (MLFMA) discretizes the equations and solves them numerically with O(NLogN) complexity, where N is the number of unknowns. For solving large-scale problems, MLFMA is parallelized on distributed-memory architectures. Despite the low complexity and parallelization, the computational requirements of MLFMA solutions grow immensely in terms of CPU time and memory when extremely-large geometries (in wavelengths) are involved. The thesis provides computational and theoretical techniques for solving large-scale electromagnetics problems with lower computational requirements. One technique is the out-of-core implementation for reducing the required memory via employing disk space for storing large data. Additionally, a pre-processing parallelization strategy, which eliminates memory bottlenecks, is presented. Another technique, MPI+OpenMP parallelization, uses distributed-memory and shared-memory schemes together in order to maintain the parallelization efficiency with high number of processes/threads. The thesis also includes the out-of-core implementation in conjunction with the MPI+OpenMP parallelization. With the applied techniques, full-wave solutions involving up to 1.3 billion unknowns are achieved with 2 TB memory. Physical optics is a high-frequency approximation, which provides fast solutions of scattering problems with O(N) complexity. A parallel physical optics algorithm is presented in order to achieve fast and approximate solutions. Finally, a hybrid integral-equation and physical-optics solution methodology is introduced.