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

• DOI: 10.54546/mlit.2021.93.21.001
• Publication Date: 2022-01-21T14:01:56Z
• Authors: G. Hristov; R. Hristova; S. Dimova; P. Armyanov; N. Shegunov; I. Puzynin; T. Puzynina; Z. Sharipov; Z. Tukhliev
• Keywords: Speedup; Decimal; Lorenz system; Double-precision floating-point format

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