Vectorizing a finite element groundwater model on the IBM 3090 VF

We describe a vector implementation of a finite element groundwater model. We have vectorized the creation of the matrices of the nodal contacts, the creation of the local stiffness and capacity matrices, and the assembly phase. In this phase we have obtained a speed-up factor of roughly 2 compared to our best scalar implementation. We use the conjugate gradient algorithm, preconditioned by an incomplete Cholesky factorization, to solve the sparse linear systems in this model. We compare two different techniques to vectorize the iterative solver. Using the ITPACK representation to store the sparse matrix coefficients, to vectorize the iterative solver, we can obtain a speeed-up of two in the solve phase on some problems. However, as opposed to the scalar code, the time required for the vectorized iterative method is sensitive to the type of mesh we use to discretize the domain. When some nodes have many more contacts than others, it is necessary to waste some arithmetics operation when using this matrix storage representation, thus obtaining a less efficient code. The calculations were performed on the IBM 3090 VF/600 at the IBM ECSEC center in Rome, Italy.