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A Simple OpenMP Scheme for Parallel Iteration Solvers in Finite Element Analysis

S.H. Ju1
Department of Civil Engineering, National Cheng-Kung University, Tainan, Taiwan, R.O.C. Phone number: 886-6-2757575-63119; Fax number: 886-6-2358542; Email:

Computer Modeling in Engineering & Sciences 2010, 64(1), 91-109.


This study develops an OpenMP scheme to parallel the preconditioned conjugate gradient methods (PCG) in shared memory computers. The proposed method is simple and systematic, so a minor change in traditional PCG methods may produce effective parallelism. At first, the global stiffness matrix is re-numbered in order to produce a parallel three-line form matrix, and a subroutine only needs to be called once in the finite element analysis. Several basic OpenMP commands are then added into the traditional incomplete Cholesky factorization (ILU) and symmetric successive over-relaxation (SSOR) codes to make the procedures of matrix multiplication, decomposition, forward substitution, and backward substitution fully parallel.


Finite element method, ILU, OpenMP, Parallel, Preconditioned conjugate gradient methods, Shared memory computers, SSOR.

Cite This Article

Ju, S. (2010). A Simple OpenMP Scheme for Parallel Iteration Solvers in Finite Element Analysis. CMES-Computer Modeling in Engineering & Sciences, 64(1), 91–109.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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