Abstract
Increasing needs for the study of complex dynamical systems require computing solutions of a large number of ordinary and partial differential time-dependent equations in near real-time. Numerical integration algorithms, which are computationally expensive and inherently sequential, are typically used to compute solutions of ordinary and partial differential time-dependent equations. This presents challenges to study complex dynamical systems in near real-time. This paper examines the challenges of computing solutions of ordinary differential time-dependent equations using the Parareal algorithm belonging to the class of parallel-in-time algorithms on various high-performance computing accelerator-based architectures and associated programming models. The paper presents the code refactoring steps and performance analysis of the Parareal algorithm on two accelerator computing architectures: the Intel Xeon Phi CPU and Graphics Processing Unit many-core architectures, and with OpenMP, OpenACC, and CUDA programming models. The speedup and scaling performance analysis are used to demonstrate the suitability of the Parareal to compute the solutions of a single ordinary differential time-dependent equation and a family of interdependent ordinary differential time-dependent. The speedup, weak and strong scaling results demonstrate the suitability of Graphical Processing Units with the CUDA programming model as the most efficient accelerator for computing solutions of ordinary differential time-dependent equations using parallel-in-time algorithms. Considering the time and effort required to refactor the code for execution on the accelerator architectures, the Graphical Processing Units with the OpenACC programming model is the most efficient accelerator for computing solutions of ordinary differential time-dependent equations using parallel-in-time algorithms.
Highlights
The study of complex systems to analyze their stability and time evolution in near real-time due to external forces or disturbances is an emerging field of research
We investigated the performance of Parareal algorithm (PRA) to solve the system of time-dependent ordinary differential equations (ODEs) representing using homogeneous and heterogeneous computing architectures
PRA is implemented on the Intel Xeon processor code-named HSW and Xeon Phi processor code-named Knights Landing (KNL) using the OpenMP programming model
Summary
The study of complex systems to analyze their stability and time evolution in near real-time due to external forces or disturbances is an emerging field of research. The research to address the computation burden in the study of complex dynamic systems is focused on using high-performance computation (HPC) techniques with traditional supercomputers to parallelize the computation of network equations or dycore solutions resulting in execution times in terms of days. Due to the availability of powerful hardware accelerators like GPUs and Xeon Phi, HPC techniques to parallelize numerical integration methods to compute solutions of ODE/PDE using time-domain decomposition [7] [8] [9] approaches in being researched. The investigation focused on developing a reliable implementation of PRA on heterogeneous architecture to solve ODEs in temporal decomposition to reduce computational time and be applied to achieve real-time or faster than real-time TSA using a large number of GPUs. In this paper, PRA is implemented using different programming models on homogeneous and heterogeneous computing architectures.
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