Christophe Geuzaine

• Full Professor
• University of Liège

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 coils is often computationally prohibitive. In this paper, we extend the foil conductor model, well-known in norm...

A quench protection study was performed on the Fusillo Demonstrator Curved Canted Cosine Theta (CCCT) dipole magnet developed at CERN. This magnet features an aperture of 236 mm and a bending radius and angle of 1 m and 90 degrees, respectively. It has an inductance of 9.14 H, a peak winding field of 3.6 T and multi-harmonic aperture field correcti...

High-temperature superconducting coils are used in various large-scale applications, like rotating machines and high-field magnets. However, modeling these coils is a complicated and time-consuming process, especially due to the non-linearity of the current–voltage characteristics of the superconductors and the complex multiphysics involved. In thi...

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 coils is often computationally prohibitive. In this paper, we extend the foil conductor model, well-known in norm...

Resonances, also known as quasi normal modes (QNM) in the non-Hermitian case, play an ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. In this paper, we present a QNM expansion for dispersive systems, recently applied to photonics but based on sixty ye...

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 intensive simulations in a Cartesian coordinate system. We show in this paper that by working instead with a h...

In this paper, we introduce two complementary approaches for the accurate prediction of AC losses in large-scale low-temperature superconducting (LTS) magnets. These methods account for the temperature rise within the LTS coil and its impact on AC losses. The first approach is multi-scale and relies on the coupling between a macroscopic homogenized...

This paper introduces the concepts of differential geometry that are necessary to establish a systematic definition for electromagnetic forces by means of a natural thermodynamic approach. It is shown that standard electromagnetic force formulae used in finite element computational electromagnetism are particular instances of that general approach....

The ability of bulk high-temperature superconductors to trap magnetic flux densities up to one order of magnitude larger than the saturation magnetization of conventional ferromagnetic materials offers the prospect of generating large magnetic flux density gradients. Combining multiple superconductors, akin to assembling a Halbach array of permanen...

HTS coils are used in various applications, however, it is complicated and time-consuming to model their multiphysics behavior. We have developed a simple homogenized method to accurately simulate HTS coils, in the context of electrothermal quench. Different numerical models are benchmarked for these computations, and they show very good agreement...

Stacks of high-temperature superconducting tape annuli can be used as magnetic shields operating efficiently for both axial and transverse fields. However, due to their layered geometry and hybrid electrical and magnetic properties, implementing models of such structures is not straightforward. In this work, we propose two different modelling appro...

Evaluating uncertainties of geological features on fluid temperature and pressure changes in a reservoir plays a crucial role in the safe and sustainable operation of high-temperature aquifer thermal energy storage (HT-ATES). This study introduces a new automated surface fitting function in the Python API (application programming interface) of Gmsh...

Due to the distribution of eddy currents inside ferromagnetic laminations, the accurate modeling of magnetic fields and losses in the laminated cores of electrical machines requires resolving individual laminations with a fine 3D discretization. This yields finite element models so huge and costly that they are unusable in daily industrial R&D. In...

In this paper, we introduce two complementary approaches for the prediction of AC losses in large-scale low-temperature superconducting (LTS) magnets subjected to slow ramp rates. These methods account for the temperature rise within the LTS coil and its impact on AC losses. The first approach is multi-scale and relies on the coupling between a mac...

Link to download: https://www.sciencedirect.com/science/article/pii/S0021999123005648?dgcid=coauthor Full waveform inversion is a seismic imaging method which requires solving a large-scale minimization problem, typically through local optimization techniques. Most local optimization methods can basically be built up from two choices: the update...

Assembling trapped-field superconducting magnets with mutually orthogonal magnetizations directions in a Halbach array configuration offers the prospect of generating both high fields and large field gradients. A major issue when assembling bulk superconductors in a Halbach array, however, consists in the alteration of the initial current density d...

This study investigates the influence of humidity on the high voltage behaviour of zinc oxide porous pellets at room temperature, using the Phase Resolved Partial Discharge (PRPD) method. The experimental configuration corresponds to the one that would be used for flash sintering cylindrical ZnO pellets at low temperatures in possibly scalable cond...

In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising opt...

In this work we demonstrate the magnetic shielding ability of a stack of YBa2Cu3O7 tape annuli. The annuli are cut from a 46 mm wide second generation coated conductor deposited on a Ni-5at.%W alloy ferromagnetic (FM) substrate. The inner bore of the stacked tapes is 26 mm and the outer diameter is 45 mm. Three samples with different height (24 mm,...

For finite element (FE) analysis of no-insulation (NI) high-temperature superconducting (HTS) pancake coils, the high aspect ratio of the turn-to-turn contact layer (T2TCL) leads to meshing difficulties which result in either poor quality mesh elements resulting in a decrease of the solution accuracy or a high number of degrees of freedom. We propo...

The presence of graphics processors (GPUs) in supercomputers constantly increased in the past decade. Finite-difference time-domain (FDTD) and discontinuous Galerkin time-domain (DGTD) are traditionally used on GPUs for their scalability; however, the limitations of past hardware required particular care in the implementation to obtain good perform...

Electromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lamination is large with respect to its thickness, field and current distributions are accurately resolved by solving a 1-D finite element magnetodynamic problem with hysteresis across half the lamination...

Resonances, also known as quasi normal modes (QNM) in the non-Hermitian case, play an ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. In this paper, we present a QNM expansion for dispersive systems, recently applied to photonics but based on sixty ye...

Using the Cauchy integral theorem, we develop the application of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer integral operator for large wave numbers. Explicit formulas for the splitting points are derived in the one-dimensional case to build suitable complex integration paths. The construction of...

LiteBIRD is the next-generation space mission for polarization-sensitive mapping of the Cosmic Microwave Background anisotropies, with observations covering the full sky in a wide frequency range (34-448 GHz) to ensure high-precision removal of polarized foregrounds. Its main goal is to constrain the contribution of primordial gravitational waves t...

In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising opt...

In applications requiring a large magnetic force, permanent magnets with non-parallel magnetization directions can be assembled in a Halbach array to generate a large gradient of magnetic flux density. The saturation magnetization of permanent magnets, however, brings a fundamental limit on the performance of this configuration. In the present work...

It is well-known that the convergence rate of non-overlapping domain decomposition methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic wave problems strongly depends on the transmission condition enforced at the interfaces between the subdomains. Transmission operators based on perfectly matched layers (PMLs)...

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 evaluated in terms of their numerical robustness and efficiency. We propose a coupled h-phi-a-formulation as an optima...

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 evaluated in terms of their numerical robustness and efficiency. We propose a coupled h-phi-a-formulation as an optima...

Accurate electromagnetic modeling of the head of a subject is of main interest in the fields of source reconstruction and brain stimulation. Those processes rely heavily on the quality of the model and, even though the geometry of the tissues can be extracted from magnetic resonance images (MRI) or computed tomography (CT), their physical propertie...

We discuss the relevance of several finite-element formulations for systems containing high-temperature superconductors (HTS) and ferromagnetic materials (FM) in the context of a 3D motor pole model, in terms of their numerical robustness and efficiency. We propose a coupled h-φ-a-formulation as an optimal choice, modeling the problem with an a-for...

This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the n...

This paper proposes a robust and effective approach to overcome a major difficulty associated to surface finite element mesh generation: the handling surfaces with irregular (singular) parametrizations such as spheres, cones or other surfaces of revolution produced by common Computer Aided Design tools. The main idea is to represent triangles incid...

Purpose This paper aims to model a three-dimensional twisted geometry of a twisted pair studied in an electrostatic approximation using only two-dimensional (2D) finite elements. Design/methodology/approach The proposed method is based on the reformulation of the weak formulation of the electrostatics problem to deal with twisted geometries only i...

The aim of this paper is to propose efficient weak coupling formulations between the boundary element method and the high-order finite element method for solving time-harmonic electromagnetic scattering problems. The approach is based on the use of a non-overlapping domain decomposition method involving optimal transmission operators. The associate...

In this article, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the $h$ - $a$ -formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The second one, the so-called $t$ - $a$ -formulation with thin-shell approximation, applies for system...

In this work, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the h-a-formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The second one, the so-called t-a-formulation with thin-shell approximation, applies for systems with thin superconduc...

This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission conditions and cross-point treatments, which cannot scale without an efficient preconditioning technique when the n...

Using the Cauchy integral theorem, we develop the application of the steepest descent method to efficiently compute the three-dimensional acoustic single-layer integral operator for large wave numbers. Explicit formulas of the splitting points are derived in the one-dimensional case to build suitable complex integration paths. The construction of a...

This article is devoted to the derivation and assessment of local Absorbing Boundary Conditions (ABCs) for numerically solving heterogeneous time-harmonic acoustic problems. To this end, we develop a strategy inspired by the work of Engquist and Majda to build local approximations of the Dirichlet-to-Neumann operator for heterogeneous media, which...

Accurate electromagnetic modelling of the head of a subject is of main interest in the fields of source reconstruction and brain stimulation. Those processes rely heavily on the quality of the model and, even though the geometry of the tissues can be extracted from magnetic resonance images (MRI) or computed tomography (CT), their physical properti...

Perfectly Matched Layers (PMLs) appear as a popular alternative to non-reflecting boundary conditions for wave-type problems. The core idea is to extend the computational domain by a fictitious layer with specific absorption properties such that the wave amplitude decays significantly and does not produce back reflections. In the context of convect...

We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before ext...

In this work, fast stochastic surrogate models are derived for extracting RL parameters of wound inductors using the Finite Element method. To this end, the Representative Volume Element (RVE) technique is employed to convert the geometrical uncertainties (e.g. due to conductor positions in the winding window) into material uncertainties (complex p...

Knowing how the solution to time-harmonic wave scattering problems depends on medium properties and boundary conditions is pivotal in wave-based inverse problems, e.g. for imaging. This paper is devoted to the exposition of a computationally efficient method, called the adjoint state method, that allows to quantify the influence of media properties...

A non-overlapping domain decomposition method is proposed to solve large-scale finite element models for the propagation of sound with a background mean flow. An additive Schwarz algorithm is used to split the computational domain into a collection of sub-domains, and an iterative solution procedure is formulated in terms of unknowns defined on the...

In this paper, we first propose a general strategy to implement the Perfectly Matched Layer (PML) approach in the most standard numerical schemes used for simulating the dynamics of nonlinear Schrödinger equations. The methods are based on the time-splitting [15] or relaxation [24] schemes in time, and FFT-based pseudospectral discretization method...

A non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-element solution of large-scale time-harmonic wave problems. It is well-known that the convergence rate of this kind of method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order...

Triangulations are an ubiquitous input for the finite element community. However, most raw triangulations obtained by imaging techniques are unsuitable as-is for finite element analysis. In this paper, we give a robust pipeline for handling those triangulations, based on the computation of a one-to-one parametrization for automatically selected pat...

Perfectly Matched Layers (PMLs) appear as a popular alternative to non-reflecting boundary conditions for wave-type problems. The core idea is to extend the computational domain by a fictitious layer with specific absorption properties such that the wave amplitude decays significantly and does not produce back reflections. In the context of convect...

Purpose The purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across su...

We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before ext...

In this paper we present an optimized weak coupling of boundary element and finite element methods to solve acoustic scattering problems. This weak coupling is formulated as a non-overlapping Schwarz domain decomposition method, where the transmission conditions are constructed through Padé localized approximations of the Dirichlet-to-Neumann map....

This paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal and polyhedral computational domains for the finite element solution of high-frequency acoustic scattering problems. While high-order absorbing boundary conditions (HABCs) are accurate for smooth fictitious boundaries, the precisi...

This paper describes a technique that allows representing thin wires in finite element models very efficiently and accurately by idealized line elements. The approach exploits the analytical solution of the problem of the wire taken in isolation to correct the finite element solution of the problem of the idealized wire with vanishing radius. The m...

The parallel finite-element solution of large-scale time-harmonic wave problems is addressed with a non-overlapping optimized Schwarz domain decomposition method (DDM). It is well-known that the efficiency of this kind of method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based...

Triangulations are an ubiquitous input for the finite element community. However, most raw triangulations obtained by imaging techniques are unsuitable as-is for finite element analysis. In this paper, we give a robust pipeline for handling those triangulations, based on the computation of a one-to-one parametrization for automatically selected pat...

Nous présentons ici le logiciel open source ONELAB de modélisation numérique par la méthode des éléments finis pour les applications photoniques. Nous illustrons à l’aide de quelques exemples une bibliothèque évolutive de modèles paramétrables couvrant une large gamme de dispositifs rencontrés en nanophotonique. Celle-ci permet d’aborder facilement...

A non-overlapping domain decomposition method is proposed to solve large-scale finite element models for the propagation of sound with a background mean flow. An additive Schwarz algorithm is used to split the computational domain into a collection of sub-domains, and an iterative solution procedure is formulated in terms of unknowns defined on the...

This paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal and polyhedral computational domains for the finite element solution of high-frequency acoustic scattering problems. While high-order absorbing boundary conditions (HABCs) are accurate for smooth fictitious boundaries, the precisi...

A 3D frame consists of three mutual orthogonal (unit) vectors, defining a local basis. There mainly exist three ways to represent 3D frames: combination of rotations, spherical harmonics and fourth order tensor. We propose here a representation carried out by the special unitary group. The article strongly relies on Du Val (1964). We first describe...

In this paper, we consider finite element models for high-temperature superconductors and compare two dual formulations, either magnetic-field conforming or magnetic-flux-density conforming. The electrical resistivity of superconductors is described by a power law and is strongly nonlinear. We compare the accuracy and the efficiency of the dual for...

Purpose Finite element (FE) models are considered for the penetration of magnetic flux in type-II superconductor films. A shell transformation allows boundary conditions to be applied at infinity with no truncation approximation. This paper aims to determine the accuracy and efficiency of shell transformation techniques in such non-linear eddy curr...

This paper presents a framework for the simultaneous application of shape and topology optimization in electro-mechanical design problems. Whereas the design variables of a shape optimization are the geometrical parameters of the CAD description, the design variables upon which density-based topology optimization acts represent the presence or abse...

This paper describes a robust and efficient method to obtain the steady-state, nonlinear behaviour of large arrays of electrically actuated micromembranes vibrating in a fluid. The nonlinear electromechanical behaviour and the multiple vibration harmonics it creates are fully taken into account thanks to a multiharmonic finite element formulation,...

In this paper, we study a high-order finite element approach to simulate an ultrahigh finesse Fabry-Pérot superconducting open resonator for cavity quantum electrodynamics. Because of its high quality factor, finding a numerically converged value of the damping time requires an extremely high spatial resolution. Therefore, the use of high-order sim...

We present a method for computing robust shape quality measures defined for finite elements of any order and any type, including curved pyramids. The measures are heuristically defined as the minimum of the pointwise quality of curved elements. Three pointwise qualities are considered: the ICN that is related to the conditioning of the stiffness ma...

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template examples, we propose and compare in detail different ways to address the numerical computation of the electromagnetic...

Sweeping-type algorithms have recently gained a lot of interest for the solution of highfrequency time-harmonic wave problems, in particular when used in combination with perfectly matched layers. However, an inherent problem with sweeping approaches is the sequential nature of the process, which makes them inadequate for efficient implementation o...

This paper demonstrates how the statistical distribution of pinning fields in a ferromagnetic material can be identified systematically from standard magnetic measurements, Epstein frame or Single Sheet Tester (SST). The correlation between the pinning field distribution and microstructural parameters of the material is then analyzed.

In electromagnetics, the finite element method has become the most used tool to study several applications from transformers and rotating machines in low frequencies to antennas and photonic devices in high frequencies. Unfortunately, this approach usually leads to (very) large systems of equations and is thus very computationally demanding. This c...

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a c...

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a c...

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled n...

Cross fields are auxiliary in the generation of quadrangular meshes. A method to generate cross fields on surface manifolds is presented in this paper. Algebraic topology constraints on quadrangular meshes are first discussed. The duality between quadrangular meshes and cross fields is then outlined, and a generalization to cross fields of the Poin...

This paper proposes a method to compute crossfields based on the Ginzburg-Landau theory. The Ginzburg-Landau functional has two terms: the Dirichlet energy of the distribution and a term penalizing the mismatch between the fixed and actual norm of the distribution. Directional fields on surfaces are known to have a number of critical points, which...

A light 3D finite element magnetodynamic a-v model of resonant wireless power transfer (WPT) coils using 3D surface impedance boundary condition (SIBC) strongly coupled with an external circuit is proposed, reflecting the importance of external circuit elements (notably capacitances) in the resonance phenomena at circuit and field levels. The compu...

We derive and analyze a mathematical model for induction hardening. We assume a nonlinear relation between the magnetic field and the magnetic induction field. For the electromagnetic part, we use the vector–scalar potential formulation. The coupling between the electromagnetic and the thermal part is provided through the temperature-dependent elec...