Recovering Numerical Reproducibility in Hydrodynamic Simulations

Abstract

HPC simulations suffer from failures of numerical reproducibility because of floating-point arithmetic peculiarities. Different computing distributions of a parallel computation may yield different numerical results. We are interested in a finite element computation of hydrodynamic simulations within the openTelemac software where parallelism is provided by domain decomposition. One main task in a finite element simulation consists in building one large linear system and to solve it. Here the building step relies on element-by-element storage mode and the solving step applies the conjugated gradient algorithm. The subdomain parallelism is merged within these steps. We study why reproducibility fails in this process and which operations have to be corrected. We detail how to use compensation techniques to compute a numerically reproducible resolution. We illustrate this approach with the reproducible version of one test case provided by the openTelemac software suite.