A Comparison Between Different Formulations for Solving Axisymmetric Time-Harmonic Electromagnetic Wave Problems

In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried out on a two-dimensional (2D) angular cross section of the problem, thus significantly reducing the computational effort. However, the transition from a full 3D problem to a 2D analysis introduces additional difficulties such as, among others, a singularity in the variational formulation. In this work, we compare and discuss different finite element formulations to deal with these obstacles. Particular attention is paid to spurious modes and to the convergence behavior when using high-order elements.Comment: 8 pages, 4 figures, pre-submission version (preprint). Scientific Computing in Electrical Engineering, SCEE 2020, Eindhoven, The Netherlands, February 202

Comparison of 2.5D finite element formulations with perfectly matched layers for solving open axisymmetric electromagnetic cavity problems

Axial symmetry in time‐harmonic electromagnetic wave problems can be exploited by considering a Fourier expansion along the angular direction, reducing fully three‐dimensional computations to two‐dimensional ones on an azimuthal cross section. While this transition leads to a significant decrease in computational effort, it introduces additional difficulties, which necessitate appropriate finite element (FE) formulations. By combining the latter with perfectly matched layers (PML), open problems can be considered. In this work, we compare and discuss the performance of different combinations of axisymmetric FE formulations and PMLs, using a dielectric sphere in open space as a test case. As an application example, a superconducting Fabry–Pérot photon trap is considered

Quadrupole Magnet Design based on Genetic Multi-Objective Optimization

This work suggests to optimize the geometry of a quadrupole magnet by means of a genetic algorithm adapted to solve multi-objective optimization problems. To that end, a non-domination sorting genetic algorithm known as NSGA-III is used. The optimization objectives are chosen such that a high magnetic field quality in the aperture of the magnet is guaranteed, while simultaneously the magnet design remains cost-efficient. The field quality is computed using a magnetostatic finite element model of the quadrupole, the results of which are post-processed and integrated into the optimization algorithm. An extensive analysis of the optimization results is performed, including Pareto front movements and identification of best designs.Comment: 22 pages, 7 figure

Modal analysis of the ultrahigh finesse Haroche QED cavity

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 simulation techniques appears appropriate. This paper considers idealized mirrors (no surface roughness and perfect geometry, just to cite a few hypotheses), and shows that under these assumptions, a damping time much higher than what is available in experimental measurements could be achieved. In addition, this work shows that both high-order discretizations of the governing equations and high-order representations of the curved geometry are mandatory for the computation of the damping time of such cavities

Numerical analysis of a folded superconducting coaxial shield for cryogenic current comparators

This paper presents a new shield configuration for cryogenic current comparators (CCCs), namely the folded coaxial geometry. An analytical model describing its shielding performance is first developed, and then validated by means of finite element simulations. Thanks to this model, the fundamental properties of the new shield are highlighted. Additionally, this paper compares the volumetric performance of the folded coaxial shield to the one of a ring shield, the latter being installed in many CCCs for measuring particle beam currents in accelerator facilities.Comment: 13 pages, 15 figure

Parallel Finite Element Assembly of High Order Whitney Forms

This paper presents an efficient method for the finite element assembly of high order Whitney elements. We start by reviewing the classical assembly technique and by highlighting the most time consuming part. This classical approach can be reformulated into a computationally efficient matrix-matrix product. We conclude by presenting numerical results on a wave guide problem

Efficient finite element assembly of high order Whitney forms

This study presents an efficient method for the finite element assembly of high order Whitney elements. The authors start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, they show how this classical approach can be reformulated into a computationally efficient matrix-matrix product. They also address the global orientation problem of the vector valued basis functions. They conclude by presenting numerical results for a three-dimensional wave propagation problem

Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms

Classically, domain decomposition methods (DDM) for time-harmonic electromagnetic wave propagation problems make use of the standard, low order, Nédélec basis functions. This paper analyzes the convergence rate of DDM when higher order finite elements are used for both volume and interface discretizations, in particular when different orders are used in the volume and on the interfaces