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The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the…

Computational Physics · Physics 2021-02-03 Alexandre Arsenault , Frédéric Sirois , Francesco Grilli

Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite element method, the use of vector-dependent variables in non-conducting domains leads to…

Computational Physics · Physics 2021-10-13 Alexandre Arsenault , Bruno de Sousa Alves , Frédéric Sirois

The growing interest in the modeling of superconductors has led to the development of effective numerical methods and software. One of the most utilized approaches for magnetoquasistatic simulations in applied superconductivity is the $H$…

Superconductivity · Physics 2023-01-31 Nicolo Riva , Alexandre Halbach , Mika Lyly , Christian Messe , Janne Ruuskanen , Valtteri Lahtinen

This paper presents a novel finite-element approach for the electromagnetic modeling of superconducting coated conductors. We combine a thin-shell (TS) method to the $H$-$\phi$ formulation to avoid the meshing difficulties related to the…

Computational Physics · Physics 2022-01-12 Bruno de Sousa Alves , Valtteri Lahtinen , Marc Laforest , Frédéric Sirois

We discuss the relevance of several finite-element formulations for nonlinear systems containing high-temperature superconductors (HTS) and ferromagnetic materials (FM), in the context of a 3D motor pole model. The formulations are…

Accelerator Physics · Physics 2024-06-25 Julien Dular , Kévin Berger , Christophe Geuzaine , Benoît Vanderheyden

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…

Computational Engineering, Finance, and Science · Computer Science 2018-04-13 Marc Olm , Santiago Badia , Alberto F. Martín

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…

This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally…

The development of the high-temperature superconductors (HTS) conductors has allowed the development of diverse superconductor devices. Some of these devises, like the power generators and high-field magnets, are classified as large-scale…

Applied Physics · Physics 2020-06-04 Edgar Berrospe-Juarez , Frederic Trillaud , Victor M R Zermeno , Francesco Grilli

Modelling high temperature superconductor (HTS) motors remains challenging mainly due to the high aspect ratio of these conductors but also because of the properties of the magnetic materials. This paper presents a 2D time dependent model…

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially…

The modeling of superconducting magnetic bearing (SMB) is of great significance for predicting and optimizing its levitation performance before construction. Although lots of efforts have been made in this area, it still remains some space…

Superconductivity · Physics 2018-08-01 Loïc Quéval , Kun Liu , Wenjiao Yang , Víctor M. R. Zermeño , Guangtong Ma

Numerical models based on the finite-element method (FEM) are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the $T$-$A$…

The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have…

Applied Physics · Physics 2019-03-01 Edgar Berrospe-Juarez , Victor M R Zermeno , Frederic Trillaud , Francesco Grilli

The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models for superconductors have evolved from simple analytical models to complex…

In recent years, numerical models have become popular and powerful tools to investigate the electromagnetic behavior of superconductors. One domain where this advances are most necessary is the 3D modeling of the electromagnetic behavior of…

Superconductivity · Physics 2020-01-10 M. Kapolka , V. M. R. Zermeño , S. Zou , A. Morandi , P. L. Ribani , E. Pardo , F. Grilli

Numerical methods for modeling thin-film magnetization are primarily focused on computing the current density distribution. The highly nonlinear current-voltage characteristic of type-II superconductors significantly complicates the…

Superconductivity · Physics 2026-05-15 Leonid Prigozhin , Vladimir Sokolovsky

The simulation of large-scale high-temperature superconducting (HTS) magnets is a computational challenge due to the multiple spatial scales involved, from the magnet to the detailed turn-to-turn geometry. To reduce the computational cost…

Accelerator Physics · Physics 2025-10-13 Louis Denis , Benoît Vanderheyden , Christophe Geuzaine

We investigate the coupling factor $\phi_\mu$ that quantifies the magnetic flux $\Phi$ per magnetic moment $\mu$ of a point-like magnetic dipole that couples to a superconducting quantum interference device (SQUID). Representing the dipole…

Superconductivity · Physics 2023-07-13 J. Linek , M. Wyszynski , B. Müller , D. Korinski , M. V. Milošević , R. Kleiner , D. Koelle

Efficient numerical models are required for the design of systems with high temperature superconductor (HTS) coils, as fully resolved finite element simulations of individual coated conductors become computationally prohibitive. This work…

Computational Engineering, Finance, and Science · Computer Science 2026-04-02 Elias Paakkunainen , Louis Denis , Benoît Vanderheyden , Christophe Geuzaine , Paavo Rasilo , Sebastian Schöps
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