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Parallel-in-Time Integration of Transient Phenomena in No-Insulation Superconducting Coils Using Parareal

Erik Schnaubelt, Mariusz Wozniak, Julien Dular, Idoia Cortes Garcia, Arjan Verweij, Sebastian Schöps

TL;DR

The paper tackles the high computational cost of transient magneto-thermal simulations for no-insulation HTS coils by applying the Parareal method with automatic time partitioning to enable parallel-in-time integration. It uses a non-intrusive, open-source FE workflow to solve a coupled system with a weak magneto-thermal formulation, including a power-law HTS resistivity and an H-phi representation. The authors demonstrate speed-ups up to $2.75$ with 16 time windows for a 3D NI pancake coil, validating the approach on realistic quench-like transients and highlighting the trade-off between coarse-propagator cost and load balancing. The work offers a practical route to faster design and safety analysis of NI HTS magnets and points to avenues for improving coarse solves and load distribution in future implementations.

Abstract

High-temperature superconductors (HTS) have the potential to enable magnetic fields beyond the current limits of low-temperature superconductors in applications like accelerator magnets. However, the design of HTS-based magnets requires computationally demanding transient multi-physics simulations with highly non-linear material properties. To reduce the solution time, we propose using Parareal (PR) for parallel-in-time magneto-thermal simulation of magnets based on HTS, particularly, no-insulation coils without turn-to-turn insulation. We propose extending the classical PR method to automatically find a time partitioning using a first coarse adaptive propagator. The proposed PR method is shown to reduce the computing time when fine engineering tolerances are required despite the highly nonlinear character of the problem. The full software stack used is open-source.

Parallel-in-Time Integration of Transient Phenomena in No-Insulation Superconducting Coils Using Parareal

TL;DR

The paper tackles the high computational cost of transient magneto-thermal simulations for no-insulation HTS coils by applying the Parareal method with automatic time partitioning to enable parallel-in-time integration. It uses a non-intrusive, open-source FE workflow to solve a coupled system with a weak magneto-thermal formulation, including a power-law HTS resistivity and an H-phi representation. The authors demonstrate speed-ups up to with 16 time windows for a 3D NI pancake coil, validating the approach on realistic quench-like transients and highlighting the trade-off between coarse-propagator cost and load balancing. The work offers a practical route to faster design and safety analysis of NI HTS magnets and points to avenues for improving coarse solves and load distribution in future implementations.

Abstract

High-temperature superconductors (HTS) have the potential to enable magnetic fields beyond the current limits of low-temperature superconductors in applications like accelerator magnets. However, the design of HTS-based magnets requires computationally demanding transient multi-physics simulations with highly non-linear material properties. To reduce the solution time, we propose using Parareal (PR) for parallel-in-time magneto-thermal simulation of magnets based on HTS, particularly, no-insulation coils without turn-to-turn insulation. We propose extending the classical PR method to automatically find a time partitioning using a first coarse adaptive propagator. The proposed PR method is shown to reduce the computing time when fine engineering tolerances are required despite the highly nonlinear character of the problem. The full software stack used is open-source.
Paper Structure (6 sections, 7 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 6 sections, 7 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Weak Magneto-Thermal Formulation
  3. Parareal Method with Automatic Partitioning of Time
  4. Numerical Example: No-Insulation HTS Coil
  5. Conclusion
  6. Acknowledgments.

Figures (3)

  • Figure 1: (left) The simulated NI coil consists of 10 turns of an HTS coated conductor surrounded by copper terminals that are used to connect to the source current. (right) Time evolution of the source current that results in a delayed central axial magnetic flux density $B_z$. The vertical, dashed lines show the division of the time intervals ${t}_j$ for $N=8$ calculated with Algorithm \ref{['Schnaubelt:algo_parareal']}.
  • Figure 2: The maximum temperature $T_\text{max}$ is shown as a result of a sequential solve with different tolerances $\text{tol}_\text{NR} = \text{tol}_t$. The absolute error $\epsilon$ of $T_\text{max}$ has been computed using a fine reference run with $\text{tol}_\text{NR} = \text{tol}_t=0.01m K$. Both graphs share the same legend.
  • Figure 3: Cumulative time taken by $\hat{\mathcal{G}}$ and $\mathcal{G}$ for all PR iterations $k$ and the minimum, average, and maximum over time windows $j$ for the cumulative time taken by $\mathcal{F}$ for all $k$. The load balancing $l$, the ratio between the minimum and maximum, is also shown.