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A High Performance Parallel Sparse Linear Equation Solver Using CUDA

Andrew J. Martin
Department of Computer Science, College of Arts and Sciences, Kent State University
Kent State University, 2011

@phdthesis{martin2011high,

   title={A High Performance Parallel Sparse Linear Equation Solver Using CUDA},

   author={Martin, A.J.},

   year={2011},

   school={Kent State University}

}

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The management of electric power systems requires continuously computing the powerflow of a power system in real-time. For large power systems, this task is often beyond the capabilities of modern CPUs. Concurrent computation is an attractive approach to accelerating it. However, the powerflow computation requires solving a large system of sparse linear equations. This problem is difficult to parallelize on classic parallel computer architectures. In this thesis I implement an algorithm that solves a system of sparse linear equations on the GPU using NVIDIA’s CUDA programming language. I develop software that randomly produces power system topologies that mimic real world systems. These power systems produce sparse matrices, which are then factorized using a method known as bi-factorization. I test my algorithm on the random power system topologies of progressively larger sizes. My experiments indicate that with a system size of 9,000 buses, my algorithm achieves a speedup of thirty-eight times over the CPU algorithm. My results demonstrate the practicality of GPU-based powerflow computation.
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