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AINV AND BILUM preconditioning techniqueS

Applied Mathematics and Mechanics(English Edition) 2004年第9期25卷 1012-1021页

作者：谷同祥迟学斌刘兴平 Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Supercomputing Center of Computer Network Information Center Chinese Academy of Science

It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

关键词： sparse matrix preconditioning technique BILUM AINV Krylov subspace method

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An Efficient CPE Preconditioner for Cyclic Structured Matrices

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Acta Mathematica Sinica,English Series 2023年第2期39卷 257-276页

作者： Jin Jing XU Xu Deng HANG Tong Xiang GU Xing Ping LIU School of Mathematics and Statistics Anhui Normal UniversityWuhu241002China Graduate School of CAEP Beijing100088China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100088China

A new cyclic pseudo-elimination(CPE,in brief)preconditioner,which combines the pseudoelimination(PE)technique and LU factorization together,is proposed for a kind of cyclic structured *** the case of M-matrices,some theoretical results of convergence and estimation of the condition number are *** experiments show that the CPE preconditioner performs the best with respect to the reduction of number of ***,it costs much less time than the ILUT and block Jacobi(BJ)preconditioners in a whole in all tested cases.

关键词： Cyclic structured matrix preconditioning technique cyclic structured mesh pseudo-elimination

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Sparse-Matrix/Canonical Grid method Combined with the SSOR Preconditioned CG Algorithm for Planar Structures Analysis

Sparse-Matrix/Canonical Grid method Combined with the SSOR P...

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2005'全国微波毫米波会议

作者： W.Zhuang,X.P.Feng L Mo and R.S.Chen Department of Communication Engineering Nanjing University of Science & Technology Nanjing 210094,P.R.China

In this paper,the microstrip structure is analyzed in terms of the mixed potential integral equation(MPIE) by using of the Rao-Wilton-Glisson(RWG) function *** integral equation is solved by the sparse-matrix/canonical grid(SMCG) method with fast Fourier transforms technique(FFT) to accelerate the matrix-vector *** algorithm reduces the memory requirement from O(N) to O(N) and the operation complexity from O(N) to O(N log N) for N *** resultant equations are then solved by the symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient(SSOR-CG) method to accelerate iteration,which converges much faster than the conventional CG *** antenna arrays are analyzed and the good results demonstrate the validity of the proposed algorithm.

关键词： Microstrip structure Sparse-Matrix/Canonical Grid preconditioning technique Conjugate-gradient method symmetric successive overrelaxation(SSOR)

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