Investigation of High-Efficiency Iterative ILU Preconditioner Algorithm for Partial-Differential Equation Systems

In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used. The ILU preconditioners of linear systems are performed on the different computation nodes of multi-central processing unit (CPU) cores. Firstly, the preconditioner of general tridiagonal matrix equations is tested on supercomputers. Then, the effects of partial-differential equation systems on the speedup of parallel multiprocessors are examined. The numerical results estimate that the parallel efficiency is higher than in other algorithms.

A Novel Adaptive Preconditioner Based CPF-GMRES Algorithm

This paper presents a novel CPF-GMRES algorithm based on an adaptive preconditioner to overcome the computational bottleneck in the analysis of large-scale power system voltage stability with CPF. Considering the combination details of CPF and GMRES, an adaptive preconditioning structure is proposed to reduce the formation times of preconditioner. Initialize the preconditioning matrix in the predictor of CPF, and modify it with Broyden method in the corrector. Large number add-in strategy and a replenished one are applied to deal with the influence of PVPQ bus-type switching. Numerical results with IEEE 118-bus test system and a real power grid verify the effectiveness of the proposed algorithm, and indicate that a remarkable speed advantage is obtained compared with the conventional CPF-GMRES with the preconditioner of ILU factorization.