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Implementing a Preconditioned Iterative Linear Solver Using Massively Parallel Graphics Processing Units

Amirhassan Asgari Kamiabad
Department of Electrical and Computer Engineering, University of Toronto
University of Toronto, 2011

@phdthesis{kamiabad2011implementing,

   title={Implementing a Preconditioned Iterative Linear Solver Using Massively Parallel Graphics Processing Units},

   author={Kamiabad, A.A.},

   year={2011},

   school={University of Toronto}

}

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The research conducted in this thesis provides a robust implementation of a preconditioned iterative linear solver on programmable graphic processing units (GPUs). Solving a large, sparse linear system is the most computationally demanding part of many widely used power system analysis. This thesis presents a detailed study of iterative linear solvers with a focus on Krylov-based methods. Since the ill-conditioned nature of power system matrices typically requires substantial preconditioning to ensure robustness of Krylov-based methods, a polynomial preconditioning technique is also studied in this thesis. Implementation of the Chebyshev polynomial preconditioner and biconjugate gradient solver on a programmable GPU are presented and discussed in detail. Evaluation of the performance of the GPU-based preconditioner and linear solver on a variety of sparse matrices shows significant computational savings relative to a CPU-based implementation of the same preconditioner and commonly used direct methods.
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