Since Sir Issac Newton determined that characterizing orbits of celestial objects required considering the gravitational interactions among all bodies in the system, the N-Body problem has been a very important tool in physics simulations. Expanding on the early use of the classical N-Body problem for gravitational simulations, the method has proven invaluable in fluid dynamics, molecular simulations and data analytics. The extension of the classical N-Body problem to solve the Helmholtz equation for groups of particles with oscillatory interactions has allowed for simulations that assist in antenna design, radar cross section prediction, reduction of engine noise, and medical devices that utilize sound waves, to name a sample of possible applications. While N-Body simulations are extremely valuable, the computational cost of directly evaluating interactions among all pairs grows quadratically with the number of particles, rendering large scale simulations infeasible even on the most powerful supercomputers. The Fast Multipole Method (FMM) and the broader class of tree algorithms that it belongs to have significantly reduced the computational complexity of N-body simulations, while providing controllable accuracy guarantees. While FMM provided a significant boost, N-body problems tackled by scientists and engineers continue to grow larger in size, necessitating the development of efficient parallel algorithms and implementations to run on supercomputers. The Laplace variant of FMM, which is used to treat the classical N-body problem, has been extensively researched and optimized to the extent that Laplace FMM codes can scale to tens of thousands of processors for simulations involving over trillion particles. In contrast, the Multi-Level Fast Multipole Algorithm (MLFMA), which is aimed for the Helmholtz kernel variant of FMM, lags significantly behind in efficiency and scaling. The added complexity of an oscillatory potential results in much more intricate data dependency patterns and load balancing requirements among parallel processes, making algorithms and optimizations developed for Laplace FMM mostly ineffective for MLFMA. In this thesis, we propose novel parallel algorithms and performance optimization techniques to improve the performance of MLFMA on modern computer architectures. Proposed algorithms and performance optimizations range from efficient leveraging of the memory hierarchy on multi-core processors to an investigation of the benefits of the emerging concept of task parallelism for MLFMA, and to significant reductions of communication overheads and load imbalances in large scale computations. Parallel algorithms for distributed memory parallel MLFMA are also accompanied by detailed complexity analyses and performance models. We describe efficient implementations of all proposed algorithms and optimization techniques, and analyze their impact in detail. In particular, we show that our work yields significant speedups and much improved scalability compared to existing methods for MLFMA in large geometries designed to test the range of the problem space, as well as in real world problems.
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