Fast and Accurate Solution of Integral Formulations of Large MQS Problems Based on Hybrid OpenMP–MPI Parallelization

Salvatore Ventre,Antonio Maffucci,Gaspare Giovinco,Fabio Villone,Francesca Cau,Andrea Chiariello

doi:10.3390/app12020627

Abstract

This paper proposes an optimal strategy to parallelize the solution of large 3D magneto-quasi-static (MQS) problems, by combining the MPI and OpenMP approaches. The studied numerical problem comes from a weak-form integral formulation of a MQS problem and is finally cast in terms of a large linear system to be solved by means of a direct method. For this purpose, two main tasks are identified: the assembly and the inversion of the matrices. The paper focuses on the optimization of the resources required for assembling the matrices, by exploiting the feature of a hybrid OpenMP–MPI approach. Specifically, the job is shared between clusters of nodes in parallel by adopting an OpenMP paradigm at the node level and a MPI one at the process level between nodes. Compared with other solutions, such as pure MPI, this hybrid parallelization optimizes the available resources, with respect to the speed, allocated memory, and the communication between nodes. These advantages are clearly observed in the case studies analyzed in this paper, coming from the study of large plasma fusion machines, such as the fusion reactor ITER. Indeed, the MQS problems associated with such applications are characterized by a huge computational cost that requires parallel computing approaches.

Highlights

Low-frequency electromagnetic problems in the so-called magneto-quasi-static (MQS)limit can be conveniently solved through numerical models coming from integral formulations, with the advantage of limiting the meshing to the conducting regions only
The proposed optimization is based on the parallelization of the tasks associated with the numerical implementation of the integral formulation, based on a hybrid OpenMP–MPI approach
A hybrid parallel computation approach implementing the joint use of MPI and OpenMP paradigms is here implemented and applied to challenging numerical magnetoquasi-static (MQS) problems

Summary

Introduction

Limit (such as, for instance, eddy current problems) can be conveniently solved through numerical models coming from integral formulations, with the advantage of limiting the meshing to the conducting regions only. There are cases of interest where the dimensions are not so large to require the use of such techniques For such cases, a direct solution method is preferable, since it provides intrinsic robustness and accuracy, with a modest increase in computational cost. The final goal of this work is the optimization of the solution of integral formulations of eddy current problems solved with direct methods, in applications where long transients must be studied, and where an effective pre-conditioning is not possible. The proposed optimization is based on the parallelization of the tasks associated with the numerical implementation of the integral formulation, based on a hybrid OpenMP–MPI approach

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Conclusion