Simulation of high temperature superconductors and experimental validation

TL;DR

This paper develops a parallel finite element framework using the H-formulation and Nédélec elements to simulate superconducting devices' electromagnetic response, validated against experiments and benchmarked for performance.

Contribution

It introduces a fully-distributed, adaptive finite element method for superconductors, combining advanced meshing, Nédélec elements, and parallel nonlinear solvers, with experimental validation.

Findings

Finite element simulations match experimental data.

The framework efficiently exploits HPC platforms.

Parallel performance is demonstrated on 3D benchmarks.

Abstract

In this work, we present a parallel, fully-distributed finite element numerical framework to simulate the low-frequency electromagnetic response of superconducting devices, which allows to efficiently exploit HPC platforms. We select the so-called H-formulation, which uses the magnetic field as a state variable. N\'ed\'elec elements (of arbitrary order) are required for an accurate approximation of the H-formulation for modelling electromagnetic fields along interfaces between regions with high contrast medium properties. An h-adaptive mesh refinement technique customized for N\'ed\'elec elements leads to a structured fine mesh in areas of interest whereas a smart coarsening is obtained in other regions. The composition of a tailored, robust, parallel nonlinear solver completes the exposition of the developed tools to tackle the problem. First, a comparison against experimental data is performed to show the availability of the finite element approximation to model the physical phenomena. Then, a selected state-of-the-art 3D benchmark is reproduced, focusing on the parallel performance of the algorithms.