In search of numerical consistency in parallel programming

Authors:
Robert W. Robey;Jonathan M. Robey;Rob Aulwes
Affiliations:
Los Alamos National Laboratory,1Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US Department of Energy und ...;University of Washington, Applied Mathematics Department, Guggenheim Hall #414, Box 352420, Seattle, WA 98195-2420, United States and Los Alamos National Laboratory,1 Computational Physics and Met ...;Los Alamos National Laboratory1, Applied Computer Science, CCS-7, MS T080, Los Alamos, NM 87545, United States
Venue:
Parallel Computing
Year:
2011

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Abstract

We present methods that can dramatically improve numerical consistency for parallel calculations across varying numbers of processors. By calculating global sums with enhanced precision techniques based on Kahan or Knuth summations, the consistency of the numerical results can be greatly improved with minimal memory and computational cost. This study assesses the value of the enhanced numerical consistency in the context of general finite difference or finite volume calculations.