Scaling Behavior of Linear Solvers on Large Linux Clusters

As high performance Linux clusters enter mainstream supercomputing, it is impor-tant to understand how well these architecture scale for important kernels in compu-tational science applications, such as linear solvers, eigenvalue solvers, multidimen-sional FFT’s. This paper attempts to characterize the scalability of state of the art linear solvers on large Linux clusters. Our studies focus on two families of algorithms, Krylov subspace methods and multigrid methods. We include results up to 256 proces-sors on a Linux cluster, with problem sizes up to 64 million unknowns.