An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned Conjugate Gradient Method using high-precision arithmetic

2017 ◽  
Vol 1 (1) ◽  
pp. 1 ◽  
Author(s):  
Sanderson L. Gonzaga De Oliveira ◽  
Alexandre A.A.M. De Abreu ◽  
Diogo Robaina ◽  
Mauricio Kischinhevsky
Keyword(s):  
High Precision ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Computational Cost ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Reordering Algorithms

Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems

2002 ◽  
Author(s):  
Noriyuki Kushida ◽  
Hiroshi Okuda ◽  
Genki Yagawa
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Singular Problems ◽  
Parallel Finite Element

In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.

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