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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…

Numerical models are powerful tools to predict the electromagnetic behavior of superconductors. In recent years, a variety of models have been successfully developed to simulate high-temperature-superconducting (HTS) coated conductor tapes.…

Superconductivity · Physics 2016-02-17 Loïc Quéval , Víctor M. R. Zermeño , Francesco Grilli

This study presents an HTS electromagnetic model combining the thin-strip, homogeneous and multi-scale methods using T-A formulation. In particular, we build the thin strips as both the analyzed HTS tapes and the boundaries of the…

Superconductivity · Physics 2022-05-18 Lei Wang , Yan Chen

The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing…

Superconductivity · Physics 2022-06-28 Carlos Roberto Vargas-Llanos , Felix Huber , Nicolo Riva , Min Zhang , Francesco Grilli

Homogenization techniques are an appealing approach to reduce computational complexity in systems containing coils with large numbers of high temperature superconductor (HTS) tapes. Resolving all the coated conductor layers and turns in…

Computational Engineering, Finance, and Science · Computer Science 2026-01-06 Elias Paakkunainen , Louis Denis , Christophe Geuzaine , Paavo Rasilo , Sebastian Schöps

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 estimation of losses in high-temperature superconductors (HTS) is fundamental during the design of superconducting devices since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D…

Superconductivity · Physics 2021-03-29 Carlos Roberto Vargas-Llanos , Francesco Grilli

In recent years, commercial HTS superconductors have gained an increasing interest for their use in applications involving large-scale superconductor systems. These systems are typically made from hundreds to thousands of turns of…

Computational Physics · Physics 2018-10-15 Edgar Berrospe-Juarez , Victor M. R. Zermeno , Frederic Trillaud , Francesco Grilli

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

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 $T$-$A$…

This article presents a review of the finite element method (FEM) model based on the $H$ formulation of Maxwell's equations used to calculate AC losses in high temperature superconductor (HTS) tapes, cables and windings for different…

Superconductivity · Physics 2020-04-22 Boyang Shen , Francesco Grilli , Tim Coombs

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

Computational Engineering, Finance, and Science · Computer Science 2024-07-29 Yuki Sato , Yuto Lewis Terashima , Ruho Kondo

A homogenization method to model a stack of second generation (2G) High Temperature Superconducting (HTS) tapes under AC applied transport current or magnetic field has been obtained. The idea is to find an anisotropic bulk equivalent for…

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms and predicting the performance of high-temperature superconductor (HTS) tapes, wires and…

Superconductivity · Physics 2013-06-27 Francesco Grilli , Enric Pardo , Antti Stenvall , Doan N. Nguyen , Weijia Yuan , Fedor Gömöry

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…

Although the H-formulation has proven to be one of the most versatile formulations used to accurately model superconductors in the finite element method, the use of vector dependent variables in non-conducting regions leads to unnecessarily…

Superconductivity · Physics 2021-04-20 Alexandre Arsenault , Frédéric Sirois , Francesco Grilli

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

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

The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays…

In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…

Numerical Analysis · Mathematics 2023-08-23 Hao Dong , Xiaofei Guan , Yufeng Nie
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