Nonlinear systems occur in diverse applications, e.g., in the steady state analysis of chemical processes. If safety concerns require the results to be provably correct then result-verifying algorithms relying on interval arithmetic should be used for solving these systems. Since such algorithms are very computationally intensive, the coarse-grained inter-box parallelism should be exploited to make them feasible in practice. In this paper we briefly describe our framework SONIC for the verified solution of nonlinear systems and give detailed information about its parallelization with OpenMP and MPI. Our numerical results show that the implemented parallelization schemes are indeed successful. The more sophisticated MPI implementation seems to be superior to the easy-to-implement OpenMP version and shows almost linear speedup up to a large number of processors.
Reliable Computing – Springer Journals
Published: Jan 1, 2006
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