论文标题
并行化多重精度泰勒串联方法用于整合洛伦兹系统
Parallelizing multiple precision Taylor series method for integrating the Lorenz system
论文作者
论文摘要
提出，实现和测试，提出了用于并行多个精确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Tiny MPIGMP库相结合。并行化的细节在洛伦兹系统的范式模型上进行了解释。我们成功在相当长的时间间隔内获得了正确的参考解决方案 - [0,7000]。通过比较〜3374小数位的第2700-阶次泰勒级数方法的结果，以及〜3510阶且精度为〜3510小数位数的结果，可以验证解决方案。在Nestum群集，索非亚，保加利亚的192个CPU核心中，第2800阶阶数计算为〜145小时，加速〜105。
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.
