The Influence of Reordering Algorithms on the Convergence of a Preconditioned Restarted GMRES Method

2020 ◽  
pp. 19-32
Author(s):  
S. L. Gonzaga de Oliveira ◽  
C. Carvalho ◽  
C. Osthoff
Keyword(s):  
Gmres Method ◽  
Reordering Algorithms ◽  
Restarted Gmres

scholarly journals A New GMRES(m) Method for Markov Chains

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bing-Yuan Pu ◽  
Ting-Zhu Huang ◽  
Chun Wen
Keyword(s):  
Markov Chain ◽  
Convergence Rate ◽  
Numerical Experiments ◽  
Gmres Method ◽  
Stationary Probability ◽  
Probability Vector ◽  
Vector Extrapolation ◽  
Restarted Gmres ◽  
Stationary Probability Vector ◽  
Irreducible Markov Chain

This paper presents a class of new accelerated restarted GMRES method for calculating the stationary probability vector of an irreducible Markov chain. We focus on the mechanism of this new hybrid method by showing how to periodically combine the GMRES and vector extrapolation method into a much efficient one for improving the convergence rate in Markov chain problems. Numerical experiments are carried out to demonstrate the efficiency of our new algorithm on several typical Markov chain problems.

GPU-accelerated preconditioned GMRES method for two-dimensional Maxwell's equations

2017 ◽  
Vol 94 (10) ◽  
pp. 2122-2144 ◽  
Author(s):  
Jiaquan Gao ◽  
Kesong Wu ◽  
Yushun Wang ◽  
Panpan Qi ◽  
Guixia He
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gmres Method ◽  
Two Dimensional ◽  
Preconditioned Gmres

The Linear System Solver of Programs Named CORTH and KYLIN2

2017 ◽  
Author(s):  
Pingzhou Ming ◽  
Junjie Pan ◽  
Xiaolan Tu ◽  
Dong Liu ◽  
Hongxing Yu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Nuclear Power ◽  
Experimental Results ◽  
Gmres Method ◽  
Thermal Hydraulics ◽  
Lattice Calculation ◽  
Minimal Residual

Sub-channel thermal-hydraulics program named CORTH and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the computing efficiency of these programs and achieving the better description on fined parameters of reactor, the programs’ structure and details are interpreted. Then the characteristics of linear systems of these programs are analyzed. Based on the Generalized Minimal Residual (GMRES) method, different parallel schemes and implementations are considered. The experimental results show that calculation efficiencies of them are improved greatly compared with the serial situation.

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