Related papers: On the Stability of Mixed Finite-Element Formulati…
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…
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…
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…
We study a non standard mixed formulation of the Poisson problem, sometimes known as dual mixed formulation. For reasons related to the equilibration of the flux, we use finite elements that are conforming in H(div) for the approximation of…
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 $T$-$A$…
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…
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…
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…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
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…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
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 Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
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…
In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of $H_0({\rm rot},\Omega)$ and a Helmholtz decomposition of its…
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…
We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the…