Abstract
This paper presents the conjugate gradient solution of large finite element systems of equations on the IBM 3090/VF vector computer utilizing polynomial preconditionings. These preconditionings are based on Saad's least square polynomials applied to a scaled system of equations. Therefore, for very ill-conditioned systems the required amount of computation is reduced. The matrix-vector operations needed in the conjugate gradient iterations, as well as in the construction of the preconditioners, are computed at element level using an element-by-element solution scheme. Reordering the finite element mesh by a colouring algorithm and stacking the finite elements for vector processing, the matrix operations are fully vectorized. To best explore the high-speed of the IBM 3090 Vector Facility, the Basic Linear Algebra Subprograms available in the ESSL vector library were invoked in the test runs. The numerical experiments provide the necessary support to efficiently use polynomial preconditionings in finite element applications.
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