Open Access

ARTICLE

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

S.H. Ju¹

1 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: juju@mail.ncku.edu.tw

Computer Modeling in Engineering & Sciences 2010, 64(1), 91-109. https://doi.org/10.3970/cmes.2010.064.091

Abstract

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.

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Keywords

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