Abstract
In this paper we study the use of conjugate gradient iterative solution techniques for the solution of sparse systems of algebraic equations generated by the problem ADINA [K.J. Bathe, Nucl. Engng Des. 98, 57–67 (1986)], as well as those resulting from a finite element discretization of fluid flow problems. The symmetric positive definite systems generated by ADINA for static structural analysis are solved with a conjugate gradient iterative method with incomplete Cholesky preconditioning. A biconjugate gradient method is used with incomplete LU factorization as a preconditioner to solve the equations with nonsymmetric coefficient matrices arising in the analysis of a fluid flow problem. The results of our numerical experiments show that preconditioned iterative methods can have significant advantages over direct methods in the solution of large, sparse systems of equations arising in 3D static structural analysis. However, the equations arising in fluid flow analysis are not as amenable to iterative solution techniques of the kind described in this paper.
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