Deterministic Random Walk: A New Preconditioner for Power Grid Analysis


Iterative linear equation solvers depend upon high-quality preconditioners to attain fast convergence. For sparse symmetric systems arising from large power grid analysis issues, but, preconditioners generated by traditional incomplete Cholesky factorization are usually of low quality, resulting in slow convergence. On the opposite hand, preconditioners generated by random walks are quite effective to reduce the quantity of iterations, though requiring considerable quantity of time to compute in a stochastic manner. We tend to propose in this paper a new preconditioning technique for power grid analysis, named deterministic random walk that mixes the advantages of the on top of two approaches. Our proposed algorithm computes the preconditioners during a deterministic manner to scale back computation time, while achieving similar quality as stochastic random walk preconditioning by modifying fill-ins to compensate dropped entries. We have proved that for such compensation theme, our algorithm can invariably succeed, that otherwise can't be guaranteed by traditional incomplete factorizations. We have a tendency to demonstrate that by incorporating our proposed preconditioner, a conjugate gradient solver is in a position to outperform a state-of-the-art algebraic multigrid preconditioned solver for dc analysis, and is terribly economical for transient simulation on public IBM power grid benchmarks.

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