"Parallelizing multiple precision Taylor series method for integrating the Lorenz system"

I. Hristov¹, R. Hristova¹, S. Dimova¹, P. Armyanov¹, N. Shegunov¹,Puzynin², T. Puzynina², Z. Sharipov², Z.Tukhliev²

 ¹Sofia University, Faculty of Mathematics and Informatics, Bulgaria

²JINR, Laboratory of Information Technologies, Dubna, Russia

A hybrid MPI+OpenMP strategy for parallelizing multiple precision Taylor series method is proposed, realized and tested. To parallelize the algorithm, we combine MPI and OpenMP parallel techniques together with the GMP library (GNU multiple precision library) and the tiny MPIGMP library. The details of the parallelization are explained on the paradigmatic model of the Lorenz system. We succeeded to compute a reliable trajectory for the Lorenz attractor in the rather long time interval [0, 7000]. The solution was checked by comparing the results for 2700-th order Taylor series method and precision ~ 3374 decimal digits with those with 2800-th order and precision ~ 3510 decimal digits. With 192 CPU cores, the 2800-th order computation lasted ~148 hours with a speedup ~103.

Information in Indico: https://indico-hlit.jinr.ru/event/211/