Performance Analysis of Accelerator Architectures and Programming Models for Parareal Algorithm Solutions of Ordinary Differential Equations

Lakshmiranganatha, Sumathi; Muknahallipatna, Suresh

doi:10.4236/jcc.2021.92003

Cited by 2 publications

(3 citation statements)

References 38 publications

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“…The modified PRA is implemented using OpenMP, OpenACC, and CUDA programming models across homogeneous and heterogeneous computing platforms. The homogeneous computing architecture comprises of Intel Xeon processor codenamed Haswell (HSW) and Xeon phi accelerator Knights Landing (KNL) while the heterogeneous computing architecture consists of Nvidia GPUs [11]. .…”

Section: Performance Resultsmentioning

confidence: 99%

“…. The optimization techniques presented in [11] are used in the implementation of the modified PRA. The homogenous architecture parallel runtime of the modified PRA is given in equation 10 addressing the modifications to the parallel runtime of the original PRA [11].…”

Section: Performance Resultsmentioning

confidence: 99%

“…The results in [10] [11] showed that a significant amount of time is spent on the predictor step computing ̃ values. This step impacted the overall performance of the original PRA and showed poor scaling when implemented on many-core and multi-core architectures for a system of inter-dependent ODEs.…”

Section: ̃=mentioning

confidence: 99%

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Modified Parareal Algorithm for Solving Time-Dependent Differential Equations

Lakshmiranganatha¹,

Muknahallipatna²

2021

World Congress on Electrical Engineering and Computer Systems and Science

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Parallel algorithms are implemented to compute the solutions of partial differential equations and ordinary differential equations of complex dynamical systems to achieve near real-time solutions. One of the parallel algorithms widely implemented is the Parareal algorithm to solve time-dependent differential equations for various scientific applications. Parareal algorithm has shown promising speedups in achieving near real-time solutions using accelerators. However, it has been observed that the sequential predictorcorrector step of the Parareal algorithm impacts the computational performance. This paper analyses the Parareal algorithm and proposes modification to the predictor-corrector step of the Parareal algorithm to exploit data parallelism more and reduce the computation time. The modified algorithm is implemented to solve two systems of interdependent ODEs. The numerical accuracy and performance analysis of the modified algorithm is shown to be same as the original Parareal. The performance analysis of the modified algorithm on two accelerator computing architectures: Intel Xeon Phi CPU and Graphical processing units with OpenMP, OpenACC, and CUDA programming models are presented. The modified algorithm demonstrates performance improvement ranging from 1.2x-2x with respect to the original Parareal algorithm.

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Section: Performance Resultsmentioning

confidence: 99%

Section: Performance Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Modified Parareal Algorithm for Solving Time-Dependent Differential Equations

Lakshmiranganatha¹,

Muknahallipatna²

2021

World Congress on Electrical Engineering and Computer Systems and Science

Self Cite

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Numerical Realization of Shallow Water Bodies’ Hydrodynamics Grid Equations using Tridiagonal Preconditioner in Areas of Complex Shape

Litvinov

Atayan

Gracheva

et al. 2023

CMIT

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Introduction. Mathematical modeling of hydrodynamic processes in shallow reservoirs of complex geometry in the presence of coastal engineering systems requires an integrated approach in the development of algorithms for constructing computational grids and methods for solving grid equations. The work is devoted to the description of algorithms that allow to reduce the time for solving SLAE by using an algorithm for processing overlapping geometry segments and organizing parallel pipeline calculations. The aim of the work is to compare the acceleration of parallel algorithms for the methods of Seidel, Jacobi, modified alternately triangular method and the method of solving grid equations with tridiagonal preconditioner depending on the number of computational nodes.Materials and Methods. The numerical implementation of the modified alternating-triangular iterative method for solving grid equations (MATM) of high dimension is based on parallel algorithms based on a conveyor computing process. The decomposition of the computational domain for the organization of the pipeline calculation process has been performed. A graph model is introduced that allows to fix the connections between neighboring fragments of the computational grid. To describe the complex geometry of a reservoir, including coastal structures, an algorithm for overlapping geometry segments is proposed.Results. It was found that the efficiency of implementing one step of the MATM on the GPU depends only on the number of threads along the Oz axis, and the step execution time is inversely proportional to the number of nodes of the computational grid along the Oz axis. Therefore, it is recommended to decompose the computational domain into parallelepipeds in such a way that the size along the Oz axis is maximum, and the size along the Ox axis is minimal. Thanks to the algorithm for combining geometry segments, it was possible to speed up the calculation by 14–27 %.Discussion and Conclusions. An algorithm has been developed and numerically implemented for solving a system of large-dimensional grid equations arising during the discretization of the shallow water bodies’ hydrodynamics problem by MATM, adapted for heterogeneous computing systems. The graph model of a parallel-pipeline computing process is proposed. The connection of water body’s geometry segments allowed to reduce the number of computational operations and increase the speed of calculations. The efficiency of parallel algorithms for the methods of Seidel, Jacobi, modified alternately triangular method and the method of solving grid equations for problems of hydrodynamics in flat areas, depending on the number of computational nodes, is compared.

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Performance Analysis of Accelerator Architectures and Programming Models for Parareal Algorithm Solutions of Ordinary Differential Equations

Cited by 2 publications

References 38 publications

Modified Parareal Algorithm for Solving Time-Dependent Differential Equations

Modified Parareal Algorithm for Solving Time-Dependent Differential Equations

Numerical Realization of Shallow Water Bodies’ Hydrodynamics Grid Equations using Tridiagonal Preconditioner in Areas of Complex Shape

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