**Main innovation**: Demonstrate that parallel-in-time algorithms such as Parareal can lead to a decreased solution time for the simulation of complex transient phenomena that occur in superconducting accelerator magnets which are used, for example, in the Large Hadron Collider at the European Organization for Nuclear Research (CERN).

Thanks to superconducting accelerator magnets, generating a high magnetic field to steer or focus particle beams in circular accelerators is achieved with relatively low energy consumption. In superconducting magnets, local transition to a normal-conducting state, for instance due to local heat generation, can lead to a thermal runaway called quench. The latter can lead to catastrophic, irreversible damage. In order to avoid this, the quench behavior of superconducting magnets is studied in detail to design protection methods to avoid a destructive thermal runaway.

Numerical tools such as the finite element (FE) method are crucial to obtain an accurate, quantitative estimation of the quench behaviour. These simulations are intrinsically multi-physics problems involving coupled electromagnetism, thermodynamics, and, eventually, solid mechanics. As a local, transient phenomenon, a quench generally requires three-dimensional simulation in time with many degrees of freedom. Furthermore, as material properties over a wide temperature range must be considered, the problem is highly non-linear. For this reason, it typically requires small time steps over a large time interval to capture the thermal runaway properly. In order to reduce the solution time, the contribution in [1] suggests using parallel-in-time (PinT) algorithms such as Parareal to decrease the solution time of FE-based quench simulations. Special focus is paid to aspects of practicability for using PinT methods on complex problems such as quench: *i)* the choice of time windows which is crucial for achieving load-balancing, *ii) *the treatment of the non-linear constitutive relations on the coarse level, and *iii) *the black-box usage of PinT algorithms for non-expert users. In preliminary results, a reduction of solution time of around factor 1.85 has been achieved using 16 time windows for the thermal sub-problem and 1.55 for the electromagnetic sub-problem using 8 time windows. The implementation is fully open-source using a Python implementation of Parareal, the FE solver GetDP and mesher Gmsh. The research will be continued on the coupled magneto-thermal quench problem using more computational resources. Parameter choices tailored to quench problems are expected to reduce the achieved solution time further. The authors hope to summarize the findings in a research article soon.

#### Publication

- E. Schnaubelt, M. Wozniak, J. Dular, I. Cortes Garcia & S. Schöps. Parallel-in-Time Integration of Transients in Superconducting Accelerator Magnets. In: 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2023), Dresden, Germany.