The FEAST indices—realistic evaluation of modern software components and processor technologies

AbstractWe examine the computational efficiency of linear algebra components in iterative solvers for grid-oriented simulations of PDEs. While the standard sparse matrix-vector (MV) techniques show significant losses of performance, especially on modern processors, our sparse banded components have the potential to exploit today's high computing power. We explain the major concepts of the FEAST software which contains such highly tuned numerical linear algebra basic components (Sparse Banded Blas) up to complete multigrid solvers, all being optimized with respect to the actual hardware platform. Based on algorithmic and computational studies, we present the FEAST indices which are indicators for the true performance of many modern processors, depending on the underlying FEM space, the problem size and the implementation style. These indices allow a new rating of the various hardware platforms with regard to different mathematical solution strategies, for academic and realistic numerical problems and ranging from ‘low cost’ PCs up to supercomputers