Abstract
This paper describes two vectorized implementations of preconditioned conjugate gradient (PCG) solvers. Sparse and diagonal matrix storage schemes are described and compared. A vectorized incomplete Choleski preconditioning is described and compared with Jacobi preconditioning. A modification to the basic no-fill incomplete Choleski method to improve performance and robustness is described. The two PCG solvers are compared with direct Choleski methods using a sparse Choleski solver from SPARSPAK and a vectorized variable-band Choleski solver developed at NASA Langley Research Center. All of the linear equation solvers are implemented in a large structural analysis finite element software system called the Computational Structural Mechanics (CSM) Testbed. The CSM Testbed is used to provide a common software system in which new methods are developed and tested. Several representative two- and three-dimensional structural analysis problems are solved using the various equation solvers. Results are given from runs made on the CONVEX C220 and CRAY 2 computer systems. Comparisons of the convergence rates for the iterative solvers as well as the computation rates, number of operations, and overall CPU time required by all of the equation solvers are given.
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