OPENMP COMPUTING OF A REFERENCE SOLUTION FOR COUPLED LORENZ SYSTEM ON [0,400]

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Obtaining a long term reference trajectory on the chaotic attractor for the coupled Lorenz system is adifficult task, due to the sensitive dependence on the initial conditions. Using the standard doubleprecision floating point arithmetic, we cannot obtain a reference solution longer than 2.5 time units.Combining OpenMP parallel technology together with GMP library (GNU multiple precision library),we parallelize the Taylor series algorithm for the coupled Lorenz system and obtain a referencesolution in the rather long time interval - [0,400]. We performed two large computations, each usingone CPU-node (32 cores), based on two Intel® Haswell processors. First computation was with 2158decimal digits of precision and 2480-th order method, and second computation was for verification -with 2254 decimal digits of precision and 2580-th order method. The needed time for the second(larger) computation was 6.3 days. The parallel speedup when using these 32 cores is 23.1 withparallel efficiency 72.1 %.

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