Studies of finite element procedures—the conjugate gradient and GMRES methods in adina and ADINA-F

Abstract

In this paper we present some experiences with the use of the conjugate gradient and GMRES iterative methods for the solution of large sparse systems of equations as recently implemented in ADINA and ADINA-F for structural and fluid flow problems. The conjugate gradient method preconditioned with the incomplete Cholesky decomposition is used for the symmetric positive definite systems resulting from structural problems. For fluid flow problems, the systems of equations are nonsymmetric and indefinite. For these systems, the biconjugate gradient and GMRES algorithms with preconditioning by incomplete LU factorization are used. The performance of the iterative methods is compared with the direct solution methods. The results from our numerical experiments show that the use of these iterative methods for large sparse systems can lead to significant reductions in storage requirements and computation times, especially for nonlinear structural dynamics problems and three-dimensional problems in general.