CREATOR @ ECCOMAS 2024; Part 2

2024/08/05

Michael Wiesheu, Sebastian Schöps and Idoia Cortes Garcia. Time Parallelization of Field-Circuit Coupled Simulations with Micro-Macro Parareal.

Conducting simulations with higher accuracy also comes with increased computational effort. Therefore, simulations in industry commonly rely on different levels of accuracy. High fidelity simulations are run in advance to determine the system behavior and optimize the model. For the real time control of the appliance, analytical models with lower fidelity are usually used, where the parameters are calculated by the prior simulations.

This work uses the Parallelization in Time (PinT) technique Parareal [1] to combine these levels of fidelity. Different examples in electromagnetic engineering are investigated. On the coarse level, an electric network model is solved in advance. Due to the model simplicity, the simulation time for this model is negligible. On the fine level, a field-circuit coupled problem is solved [2]. This can then be done in parallel to reduce the effective simulation time.

[1] J.-L. Lions, Y. Maday, and G. Turinici, A parareal in time discretization of PDEs. Comptes Rendus de l’Academie des Sciences – Series I – Mathematics, Vol. 332, pp. 661–668, 2001.

[2] I. Cortes Garcia, I. Kulchytska-Ruchka and S. Sch¨ops, Efficient Simulation of Field/Circuit Coupled Systems With Parallelized Waveform Relaxation. IEEE Trans actions on Magnetics, Vol. 56, pp. 1-4, 2020.

Guilherme Henrique Teixeira and Benjamin Marussig. Comparison of integration methods for trimmed elements.

Using an interface inserted in a background mesh is an alternative way of constructing a parametric shape for complex geometries without having to deal with multiple patches. However, this process may require the integration of elements cut by the interface. Our study focuses on compare the integration of cut elements defined by implicit and parametric curves. We compare the efficiency and robustness of open-source tools such as Algoim (a library for quadrature on implicitly defined geometries) and Ginkgo (a library for isogeometric analysis on Boolean operations) with numerical examples computing the area defined by the interface and benchmarks for 2D elasticity problem using the open-source code GeoPDEs . The results show us that both approaches obtain similar behaviour, the choice between the type of interface remaining dependent on the problem studied and not on the numerical aspects of the integration

Andreas Grendas, Micheal Wiesheu, Sebastian Schöps and Benjamin Marussig. Isogeometric Analysis for 2D Magnetostatic Computations with Multi-level Bézier Extraction for Local Refinement.

Local refinement is vital for efficient numerical simulations. In the context of CAD- based discretization methods such as Isogeometric Analysis (IGA), hierarchical B-splines have gained prominence. The work extends the methodology to truncated hierarchical B-splines (THB-splines) as they keep additional properties. The framework is further enriched with B ́ezier extraction, resulting in the Multi-level B ́ezier extraction method. Converting these hierarchical splines into the representation of B ́ezier elements simplifies their seamless integration into existing finite element (FE) codes. We apply this discretization method to 2D magnetostatic problems. The implementation is based on an open-source Octave/MATLAB IGA code called GeoPDEs, which allows us to compare our routines with globally refined spline models as well as locally refined ones where the solver does not rely on B ́ezier extraction.