# Accelerated Steady-State Torque Computation for Induction Machines using Parallel-In-Time Algorithms

## TL;DR

This paper introduces a parallel-in-time algorithm, PP-IC, for rapid steady-state torque computation in induction machines, demonstrating significant acceleration and robustness over traditional methods.

## Contribution

The paper presents a non-intrusive, parallel-in-time algorithm, PP-IC, specifically designed for efficient steady-state analysis of time-periodic induction machine problems.

## Key findings

- Achieved up to several dozen times acceleration in simulations.
- Demonstrated robustness and efficiency over existing time-periodic methods.
- Validated approach on real-world induction motor data from Robert Bosch GmbH.

## Abstract

This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations via non-intrusive parallelization in time domain, i.e., existing implementations can be reused. Superiority of this parallel-in-time method is in its direct applicability to time-periodic problems, compared to, e.g, the standard Parareal method, which only solves an initial-value problem, starting from a prescribed initial value. PP-IC is exploited here to obtain the steady state of several operating points of an induction motor, developed by Robert Bosch GmbH. Numerical experiments show that acceleration up to several dozens of times can be obtained, depending on availability of parallel processing units. Comparison of PP-IC with existing time-periodic explicit error correction method highlights better robustness and efficiency of the considered time-parallel approach.