A STOPPING CRITERION FOR ITERATIVE SOLUTION OF STOCHASTIC GALERKIN MATRIX EQUATIONS

2016 ◽  
Vol 6 (3) ◽  
pp. 245-269 ◽  
Author(s):  
Christophe Audouze ◽  
Par Hakansson ◽  
Prasanth B. Nair
Keyword(s):  
Iterative Solution ◽  
Matrix Equations ◽  
Stopping Criterion ◽  
Stochastic Galerkin

scholarly journals Iterative solution of two matrix equations

1999 ◽  
Vol 68 (228) ◽  
pp. 1589-1604 ◽  
Author(s):  
Chun-Hua Guo ◽  
Peter Lancaster
Keyword(s):  
Iterative Solution ◽  
Matrix Equations

scholarly journals An Efficient Reduced Basis Solver for Stochastic Galerkin Matrix Equations

2017 ◽  
Vol 39 (1) ◽  
pp. A141-A163 ◽  
Author(s):  
C. E. Powell ◽  
D. Silvester ◽  
V. Simoncini
Keyword(s):  
Matrix Equations ◽  
Reduced Basis ◽  
Stochastic Galerkin

Stopping Criterion in Iterative Solution Methods for Reynolds Equations

2010 ◽  
Vol 53 (5) ◽  
pp. 739-747 ◽  
Author(s):  
Nenzi Wang ◽  
Shih-Hung Chang ◽  
Hua-Chih Huang
Keyword(s):  
Iterative Solution ◽  
Stopping Criterion ◽  
Reynolds Equations ◽  
Solution Methods ◽  
Iterative Solution Methods

Enhanced alternating energy minimization methods for stochastic galerkin matrix equations

2022 ◽  
Author(s):  
Kookjin Lee ◽  
Howard C. Elman ◽  
Catherine E. Powell ◽  
Dongeun Lee
Keyword(s):  
Energy Minimization ◽  
Matrix Equations ◽  
Minimization Methods ◽  
Stochastic Galerkin

Fast Convergence of Iterative Computation for Incompressible-Fluid Reynolds Equation

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Nenzi Wang ◽  
Kuo-Chiang Cha ◽  
Hua-Chih Huang
Keyword(s):  
Reynolds Equation ◽  
Truncation Error ◽  
Solution Method ◽  
Iterative Solution ◽  
Stopping Criterion ◽  
Iterative Computation ◽  
Grid Convergence ◽  
Grid Convergence Index ◽  
Successive Over Relaxation ◽  
Iterative Solution Method

When a discretized Reynolds equation is to be solved iteratively at least three subjects have to be determined first. These are the iterative solution method, the size of gridwork for the numerical model, and the stopping criterion for the iterative computing. The truncation error analysis of the Reynolds equation is used to provide the stopping criterion, as well as to estimate an adequate grid size based on a required relative precision or grid convergence index. In the simulated lubrication analyses, the convergent rate of the solution is further improved by combining a simple multilevel computing, the modified Chebyshev acceleration, and multithreaded computing. The best case is obtained by using the parallel three-level red-black successive-over-relaxation (SOR) with Chebyshev acceleration. The speedups of the best case relative to the case using sequential SOR with optimal relaxation factor are around 210 and 135, respectively, for the slider and journal bearing simulations.

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