A three-dimensional Hybrid High-Order method for magnetostatics

International audienceWe introduce a three-dimensional Hybrid High-Order method for magnetostatic problems. The proposed method is easy to implement, supports general polyhedral meshes, and allows for arbitrary orders of approximation

A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics

We prove a discrete version of the first Weber inequality on three-dimensional hybrid spaces spanned by vectors of polynomials attached to the elements and faces of a polyhedral mesh. We then introduce two Hybrid High-Order methods for the approximation of the magnetostatics model, in both its (first-order) field and (second-order) vector potential formulations. These methods are applicable on general polyhedral meshes, and allow for arbitrary orders of approximation. Leveraging the previously established discrete Weber inequality, we perform a comprehensive analysis of the two methods. We finally validate them on a set of test-cases

Modelling and optimisation of magnetic circuits for next generation Hall-effect thrusters

Within electric propulsion, Hall-effect thrusters are an attractive alternative to chemical propulsion for low-thrust applications. The applied magnetic field in Hall thrusters is a relevant part of the design process, on which studies are conducted for erosion reduction, among others. The present thesis is focused on the magnetic topology of next generation Hall-effect thrusters. A magnetostatics simulation tool for axisymmetric problems is developed on the basis of the Finite Element Method Magnetics solver, with which it is possible to attain different topographies, as the so known as singular-point and, within Erosion Reduction Strategies (ERS), the magnetic shielding. In addition, the tool allows for the launching of several simulations in series (a batch), in which different parameters may be modified from one case to the next. In the line of the development of magnetic circuits, a parametric study on coil design is performed, revealing the parameters necessary to fulfil geometric and electric current constraints on coils. The analysis allows for the design of a circuit feasible to be manufactured if properly translated from the axisymmetric model to a three-dimensional geometry, furthermore with the possibility of mass or power optimisation. Finally, a scaling process on the basis of an existing device is performed to design a low-power Hall thruster, of which main design parameters, and, building on them, a suitable magnetic circuit, are obtained.Grado en Ingeniería Aeroespacia

A three-dimensional Hybrid High-Order method for magnetostatics

International audienceWe introduce a three-dimensional Hybrid High-Order method for magnetostatic problems. The proposed method is easy to implement, supports general polyhedral meshes, and allows for arbitrary orders of approximation

Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem

Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method (ncVEM) and the Weak Galerkin (WG) method. HHO provides various valuable assets such as simple construction, support for fully-polyhedral meshes and arbitrary polynomial order, great computational efficiency, physical accuracy and straightforward support for hp-refinement. In this work we propose an HHO method for the indefinite time-harmonic Maxwell problem and we evaluate its numerical performance. In addition, we present the validation of the method in two different settings: a resonant cavity with Dirichlet conditions and a parallel plate waveguide problem with a total/scattered field decomposition and a plane-wave boundary condition. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter

An exterior calculus framework for polytopal methods

We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions of the de Rham complex of differential forms built on meshes made of general polytopal elements. Both constructions benefit from the high-level approach of polytopal methods, which leads, on certain meshes, to leaner constructions than the finite element method. We establish commutation properties between the interpolators and the discrete and continuous exterior derivatives, prove key polynomial consistency results for the complexes, and show that their cohomologies are isomorphic to the cohomology of the continuous de Rham complex

A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems

We present a Virtual Element Method for the 3D linear elasticity problems, based on Hellinger-Reissner variational principle. In the framework of the small strain theory, we propose a low-order scheme with a-priori symmetric stresses and continuous tractions across element interfaces. A convergence and stability analysis is developed and we confirm the theoretical predictions via some numerical tests.Comment: submitted to CMAM