“Brute-Force” Solution of Large-Scale Systems of Equations in a MPI-PBLAS-ScaLAPACK Environment

Abstract

Space-borne gravity field recovery requires the solution of large-scale linear systems of equations to estimate tens of thousands of unknown gravity field parameters from tens of millions of observations. Satellite gravity data can only be exploited efficiently by the adaption of HPC technologies. The extension of the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission, in particular, poses unprecedented computational challenges in geodesy. In continuation of our work presented in the annual report in 2010, we succeeded in the preparation of a distributed memory version of our program using the MPI, PBLAS and ScaLAPACK programming standards. The tailored implementation enhances the range of usable computer architectures to computers with less memory per node than the NEC SX-8 and SX-9 systems we used. We present implementation details and runtime results using the NEC SX systems as distributed memory systems. A comparison with our OpenMP version shows that the MPI implementation of our program brings forth a speedup of around 12% for large-scale problems.