Design and Implementation of A Hybrid Solver on CPU and GPU Multi-target Machines

doi:10.16182/j.issn1004731x.joss.21-1317

Abstract

Abstract:

The traditional parallel solving methods for the ordinary differential equations mainly include the task-oriented parallelism and the method-oriented parallelism. However, these two solving algorithms have serious shortcomings, which can only use CPU resource or just design for the homogeneous form of ODE(ordinary differential equations) clusters. By using RIDC(revisionist integral deferred correction) algorithm, a hybrid solver based on CPU and GPU multi-target machine is designed, which solves the differential equation system based on the pipeline form. Meanwhile, the parallel calculation within a single equation group and between the different equation groups is realized, which can give full play to the multi-core advantage of GPU, and also help to balance the load inside the computing node. The simulation experiments verify the efficiency, accuracy and precision of the framework.

Key words: ordinary differential equation, hybrid solver, multi-target machine, CPU, GPU

CLC Number:

TP391.9

Lin Ma, Xuesong Zhang, Xinlin Lei, Tie Bao. Design and Implementation of A Hybrid Solver on CPU and GPU Multi-target Machines[J]. Journal of System Simulation, 2022, 34(4): 670-678.

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处理器	显式欧拉	龙格库塔	隐式欧拉
CPU	0.03	0	0.02
GPU	0	0	0.01

采样点数(方程数2)	CPU单线程显式欧拉4阶	CPU单线程RK4阶	GPU显式欧拉算法
100	0.018 8	0.006 4	0.026 6
1 000	0.151 4	0.052 0	0.221 8
10 000	1.854 2	0.628 4	2.063 9
100 000	18.395 6	6.258 4	20.161 0

采样点数(方程数10)	CPU单线程显式欧拉4阶	CPU单线程RK4阶	GPU显式欧拉算法
100	0.031 0	0.012 8	0.049 8
1 000	0.304 4	0.130 4	0.451 6
10 000	3.038 3	1.298 8	4.312 1
100 000	30.305 6	12.986 4	43.526 8

采样点数(方程数2)	CPU单线程隐式欧拉4阶	GPU隐式欧拉4阶	CPU单线程隐式欧拉8阶	GPU隐式欧拉8阶
100	0.814 6	0.286 2	4.334 6	0.933 6
1 000	5.588 4	2.644 8	31.725 0	8.930 8

采样点数(方程数10)	CPU单线程隐式欧拉4阶	GPU隐式欧拉4阶	CPU单线程隐式欧拉8阶	GPU隐式欧拉8阶
100	13.498 4	0.671 8	69.640 8	2.132 2
1 000	85.591 6	6.331 6	483.671 8	20.578 2