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This study aims to enhance the parallel performance of a parallel-in-space-and-time (PinST) finite-element method (FEM) using time step overlapping. The effectiveness of the developed method is clarified in a magnet eddy-current loss analysis of a practical interior permanent magnet synchronous motor (IPMSM) using a massively parallel computing environment.

The developed PinST FEM is a combination of the domain decomposition method as a parallel-in-space (PinS) method and a parallel time-periodic explicit error correction (PTP-EEC) method, which is one of the parallel-in-time (PinT) approaches. The parallel performance of the PinST FEM is further improved by overlapping the time steps with different processes in the PTP-EEC method.

By applying the overlapping PTP-EEC method, the convergence of the transient solution to its steady state can be accelerated drastically. Consequently, the good parallel performance of the PinST FEM is achieved in magnetic field analyses of the practical IPMSM using a massively parallel computing environment, in which over 10,000 processes are used.

In this study, the PinST FEM based on time step overlapping is newly developed and its effectiveness is demonstrated in a massively parallel computing environment, in which using either the PinS or PinT method alone cannot achieve sufficient parallel performance. This finding implies a new direction of parallel computing approaches for electromagnetic field computation.

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.