Conference Agenda

OA2: Mathematical modelling and formulations
Tuesday, 16/Jul/2019:
4:30pm - 6:10pm

Session Chair: Jan Sykulski
Session Chair: Stephane Clenet
Location: Auditorium

4:30pm - 4:50pm

Exact Modal Expansion using Dispersive Quasi Normal Modes (DQNM) of open and periodic nanophotonic structures

Minh Duy Truong2, Guillaume Demésy1, Frédéric Zolla1, André Nicolet1

1Aix-Marseille Université, France; 2CNRS, France

In this paper we present recent developments in our modal expansion technique for electromagnetic structures with highly dispersive media and its application in unbounded geometries. The formulas, based on a simple version of the Keldyˇs theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly non reciprocal. A dispersive benchmark case, a diffraction grating, made of a periodic slit array etched in a free-standing silver membrane, is presented.

4:50pm - 5:10pm

Finite element formulations for systems with high-temperature superconductors and soft ferromagnetic materials

Julien Dular, Christophe Geuzaine, Benoit Vanderheyden

University of Liège, Institut Montefiore B28, Dept. of Electrical Engineering and Computer Science, B-4000 Liège, Belgium

Modelling systems containing high-temperature superconductors and ferromagnetic materials requires to handle their nonlinear constitutive laws. Many numerical methods are possible but not all of them offer reliable results and efficient simulations. In this work, we investigate different finite element formulations (h-conform and b-conform) and linearization techniques. We show that none of the methods is optimal for modelling both materials at the same time and we propose a coupled formulation that exploits the best method for each material. The proposed coupled formulation is shown to be more efficient in all tested situations.

5:10pm - 5:30pm

Diagonal material matrices for arbitrary simplicial meshes for solving Poisson problems with one unknown per element

Fabrizio Bellina, Ruben Specogna

EMCLab, DPIA, Università di Udine, Italy

We present a technique to extend the geometric construction of diagonal material matrices-known also as diagonal discrete Hodge operators-to arbitrary triangular and tetrahedral meshes and arbitrary material parameters.

The proposed material matrices are tailored to enable the use of a complementary-dual formulation for Poisson problems with one unknown per element.

5:30pm - 5:50pm

Implementation of High Order on Surface Radiation Boundary Conditions

Nathan Ida, Nassif Berrabah, Subramania Hariharan

The university of Akron, United States of America

Electromagnetic scattering problems that involve far-field radiation patterns and the calculations of total currents induced in a per-fect conductor can be solved using local radiation boundary conditions. These local conditions are often imposed on a domain enclosing the scatterer and the typical finite element methods are incorporated so that the well-posedness of the modified problems encompassing the local radiation boundary conditions is preserved. Much effort in recent years has been devoted to attempts to construct higher order far field conditions, so that the solution accuracy can be improved. In this work, we avoid extensive computations, and bring the radiation boundary on the scatter’s surface itself. This procedure is known as the On Surface Radiation Boundary Condition (OSRBC). The limitations in the past have been he implementable order of the OSRBC. Regardless, the key feature of the OSRBC to calculate the relevant quantities for engineers is the normal derivative of the solution on the OSRBC. The present work introduces a new method for calculation of the normal derivative of the electric field on the surface of a scatterer of known shape. The method is based on a formulation of the boundary conditions through a recursive sequence of differential operators. The numerical implementa-tion of this formulation allows one to extract a relation which is then used to solve for the quantity of interest, such as radar cross-section.

5:50pm - 6:10pm

Hybrid Kinetic-MHD Simulations of Vacuum Arc Based on Field-Circuit Coupling Method

Feng Chen, Yudong Xu, Zhiyuan Cao, Zhenxing Wang, Lin Yin

Xi'an Jiaotong University, China, People's Republic of

This paper deals with the numerical simulation of vacuum arc based on the field-circuit coupling model. This type of arc is typically found in vacuum interrupters and simulated by the kinetic-MHD hybrid computational model. In the hybrid model, the dynamics of electron is simplified by equating electrons to massless fluids, while the kinetic dynamics of ions is described by equating ions to macroparticles. The hybrid model can illustrate the self-consistent propagation of particles and electromagnetic fields in the vacuum interrupter. Moreover, the coupling model with the external circuit can ensure self-consistent calculation results.