| The research conducted in this thesis provides a robust implementation of a preconditioned iterative linear solver on programmable graphic processing units (GPUs), appropriately designed to be used in electric power system analysis. Solving a large, sparse linear system is the most computationally demanding part of many widely used power system analysis, such as power flow and transient stability. 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. Programmable GPUs currently offer the best ratio of floating point computational throughput to price for commodity processors, outdistancing same-generation CPUs by an order of magnitude. This has led to the widespread adoption of GPUs within a variety of computationally demanding fields such as electromagnetics and image processing. 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, ranging in size from 30 x 30 to 3948 x 3948, shows significant computational savings relative to a CPU-based implementation of the same preconditioner and commonly used direct methods. |
