Session
| ||

OA2: Mathematical modelling and formulations
| ||

Presentations
| ||

4:30pm - 4:50pm
Exact Modal Expansion using Dispersive Quasi Normal Modes (DQNM) of open and periodic nanophotonic structures
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 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 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 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 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. |