Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

Yasuhito Takahashi (Department of Electrical Engineering, Doshisha University, Kyotanabe, Japan)
Koji Fujiwara (Department of Electrical Engineering, Doshisha University, Kyotanabe, Japan)
Takeshi Iwashita (Information Initiative Center, Hokkaido University, Sapporo, Japan)
Hiroshi Nakashima (Academic Center for Computing and Media Studies, Kyoto University, Kyoto, Japan)



This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment.


First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors.


The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost.


This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.



Takahashi, Y., Fujiwara, K., Iwashita, T. and Nakashima, H. (2019), "Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , Vol. ahead-of-print No. ahead-of-print.

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