Parallel block-diagonal preconditioning of finite element consolidation equations

Matrix preconditioning is an important preliminary operation for the most efficient solution to sparse Finite Element (FE) consolidation equations by a projection (or conjugate gradient like) solver. In a parallel computing environment block-diagonal preconditioning appears particularly attractive as it may take advantage of the block-matrix-vector products to be executed concurrently on parallel processors. In the present communication FE consolidation models with a size up to 100000 are solved by TFQMR (Transpose Free Quasi Minimal Residual) preconditioned with block diagonal matrices of size 1, 5, 10 and 15. The results from a number of numerical experiments show that convergence is generally improved, and especially so for the largest problems, by increasing the block size. The speed-up ranges between 3 and 4 with 16 processors pointing to a satisfactory parallelization of the solver despite the granularity and the high sparsity of the FE consolidation models.