title: Parallel-in-Time Simulation of Electromagnetic Energy Converters
Creators: name: Kulchytska-Ruchka, Iryna
Publisher: name: UNSPECIFIED
Year: 2021

description: Computer-aided simulations are widely used in industry, as they allow to optimize the design and to understand the life cycle of engineering products, before their physical prototypes are constructed. Such simulations must be typically performed in the time domain and are especially then time consuming, when long time intervals have to be computed, e.g., until the steady state. Parallel-in-time methods such as the Parareal algorithm are powerful candidates for an acceleration of these development stages due to their capability to distribute the workload among multiple processing units. This dissertation develops and analyzes novel efficient Parareal-based approaches, particularly suitable for applications in electrical engineering such as pulse-width modulated (PWM) power converters, electric motors or transformers. The main contributions of this thesis are the following. First, a multirate Parareal method is proposed for parallel-in-time solution of systems excited with PWM signals. The idea of the approach is to solve a surrogate model with a smooth excitation on the coarse level, while on the fine level the original discontinuous PWM excitation is used. Convergence analysis gives an error estimate in terms of the deviation of the coarse input form the PWM signal. Numerical study for an RL-circuit model is in agreement with the theoretical derivations. An extension of the method to time-periodic problems is proposed and analyzed for a linear model problem. The multirate Parareal-based methods are applied to a buck converter and a four-pole induction machine. Second, time parallelization with Parareal is incorporated into an industrial simulation tool and used for the design of an electric vehicle drive. In contrast to many other methods Parareal is not limited to particular operating points or motor configurations and can employ already existing solvers due to its non-intrusiveness. By means of a periodic Parareal method and 80 cores, the steady state of the motor can be obtained up to 28 times faster compared to the sequential calculation. This is a great aid to industry as it speeds up the design workflow significantly. Such a good performance of Parareal for induction machine simulations is justified also based on an eigenvalue analysis of two circuit schemes in this thesis. Third, a parallel-in-time algorithm for time-periodic problems based on a multi-harmonic coarse grid correction is presented. It introduces an additional parallelization on the coarse level due to a Newton-based linearization with a block-cyclic Jacobian matrix, followed by a frequency-domain transformation. Convergence analysis is performed for a model problem and confirmed by a numerical study. Application to a nonlinear coaxial cable model and a nonlinear transformer model yields acceleration of the sequential computations up to factors of 175 when exploiting 20 cores. Finally, this thesis develops a Parareal-based approach for time-periodic problems with unknown period as, e.g., autonomous evolution systems. The method is tested on a Colpitts oscillator model.