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 technologies together with GMP library (GNU miltiple precision libary) and the tiny MPIGMP library. The details of the parallelization are explained on the paradigmatic model of the Lorenz system. We succeed to obtain a correct reference solution in the rather long time interval - [0,7000]. The solution is verified by comparing the results for 2700-th order Taylor series method and precision of ~ 3374 decimal digits, and those with 2800-th order and precision of ~ 3510 decimal digits. With 192 CPU cores in Nestum cluster, Sofia, Bulgaria, the 2800-th order computation was ~ 145 hours with speedup ~ 105.

中文翻译：

---

用于积分洛伦兹系统的并行化多精度泰勒级数方法

提出、实现并测试了一种用于并行化多精度泰勒级数方法的混合 MPI+OpenMP 策略。为了并行化算法，我们将 MPI 和 OpenMP 并行技术与 GMP 库（GNU miltiple precision libary）和微型 MPIGMP 库结合在一起。在洛伦兹系统的范式模型上解释了并行化的细节。我们成功地在相当长的时间间隔内获得了正确的参考解 - [0,7000]。通过比较 2700 阶泰勒级数方法的结果，精度为约 3374 位十进制数，与 2800 阶和精度为约 3510 位十进制数的结果，验证了该解决方案。在保加利亚索非亚的 Nestum 集群中有 192 个 CPU 内核，2800 阶计算时间约为 145 小时，加速约为 105。