Thin-shell approach for modeling superconducting tapes in the H-φ finite-element formulation

Bruno De Sousa Alves*, Valtteri Lahtinen, Marc Laforest, Frédéric Sirois

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


This paper presents a novel finite-element (FE) approach for the electromagnetic modeling of superconducting coated conductors with transport currents. We combine a thin-shell (TS) method to the H-φ-formulation to avoid the meshing difficulties related to the high aspect ratio of these conductors and reduce the computational burden in simulations. The interface conditions in the TS method are defined using an auxiliary 1-D FE discretization of N elements along the thinnest dimension of the conductor. This procedure permits the approximation of the superconductor's nonlinearities inside the TS in a time-transient analysis. Four application examples of increasing complexity are discussed: (1) single coated conductor, (2) two closely packed conductors carrying anti-parallel currents, (3) a stack of 20 superconducting tapes and (4) a full representation of a high-temperature superconducting tape comprising a stack of thin films. In all these examples, the profiles of both the tangential and normal components of the magnetic field show good agreement with a reference solution obtained with the standard 2-D H-φ-formulation. Results are also compared with the widely used T-A-formulation. This formulation is shown to be dual to the TS model with a single FE (N = 1) in the auxiliary 1-D systems. The increase of N in the TS model is shown to be advantageous at small inter-tape separation and low transport current since it allows the tangential components of the magnetic field to penetrate the thin region. The reduction in computational cost without compromising accuracy makes the proposed model promising for the simulation of large-scale superconducting applications.

Original languageEnglish
Article number024001
Pages (from-to)1-14
Number of pages14
JournalSuperconductor Science and Technology
Issue number2
Publication statusPublished - Feb 2022
MoE publication typeA1 Journal article-refereed


  • finite-element method
  • high-temperature superconductors
  • thin-shell approach
  • transient analysis


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