high performance computing on graphics processing units: hgpu.org

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.