Abelin Kameni

A time domain nodal discontinuous Galerkin method is used to solve Maxwell equations and simulate reflectometry responses of soft faults. In this paper shielding defects of coaxial cables or other shielded lines are considered. Hexahedral high order elements are used for meshing. They allow to avoid bulky meshes compared to tetrahedral elements. A gaussian pulse is injected on the faulty line. The reflectogram of the line containing the chafing soft defect is obtained and parameters such as the reflection coefficient or the characteristic impedance of the fault are computed. These numerical values are compared to those obtained in experimental investigations. The experimental impedances estimated using a classical transmission matrix method are in very good agreement with those obtained by three-dimensional modeling..

ABSTRACT Complete penetration magnetic field $B_P$ is a feature of a superconducting sample submitted to an applied magnetic field. It is very important to know this for applications such as an electrical motor or levitation. The electric $E$– $J$ characteristics of a high-temperature superconductor (HTS) bulk is generally described by a power law. The main purpose of this paper is to investigate the influence of the $n$-value and the applied magnetic field rise rate $V_b$ on the $B_P$ of a cylindrical HTS pellet. The numerical results presented come from the resolution of a nonlinear diffusion problem with commercial software. In this paper, cylindrical HTS pellets are submitted to an axial applied magnetic field. With the help of these simulations, a linear relationship between $B_P,V_b$, and the $n$-value has been found. A comparison between measurements and simulations is done for the magnetization of cylindrical bulk superconducting samples. This comparison allows to determine the critical current density $J_C$ and $n$-value of the power law $E(J)=E_C(J/J_C) n$. The experiment is based on the direct measurement of the local magnetic field in the gap between two bulk HTS pellets. The f- eld penetration measurements have been carried out on HTS pellets at 77 K by applying increasing magnetic fields with a quasi-constant sweep rate for the axial direction of the applied magnetic field. Two values of complete penetration magnetic field $B_P$ have been measured at two different rise rates $V_b$. The $n$-value of the real HTS pellet has been deduced.

ABSTRACT SUMMARY In this paper, different formulations of Maxwell equations are combined for computing the shielding effectiveness of enclosures made from heterogeneous periodic materials. The validity of the homogenized parameters given by Maxwell-Garnett rules in the frequency domain are tested in the time domain by using a nodal DG method, which uses an interface condition based on analytical solution in the frequency domain to replace a conductive sheet. This interface condition allows to avoid meshing the thin sheet, thus reducing the computational cost. Results of scattering by composite enclosures are presented in the frequency domain thanks to a FFT. Copyright © 2013 John Wiley & Sons, Ltd.

ABSTRACT A semi-implicit approach is proposed for computing the current density in superconductors characterized by nonlinear vectorial power law. A nodal discontinuous Galerkin method is adopted for the spatial discretization of the nonlinear system satisfied by the components of the electric field. Explicit developments are used to construct boundary conditions to avoid the modeling of a volume around the superconducting sample. A modified Newton iterative method is introduced for solving the discrete system. Numerical examples on a 2-D superconducting plate and a 3-D superconducting cube are computed. Distributions of a component of the current density are presented and differences in the diffusive process are highlighted. The penetration time and losses are compared with those obtained with an $A{-}V$ formulation solved by a finite-volume method.

ABSTRACT A discontinuous Galerkin method is proposed for computing the current density in superconductors characterized by a constitutive power law between the current density and the electric field. The method is formulated to solve the nonlinear diffusion problem satisfied by the electric field, both in the scalar and 2-D vectorial case. Application examples are given for a superconducting cylinder subjected to an external magnetic field. Results are compared to those given by the mixed finite-element/finite-volume method and those obtained using a standard finite-element software. Efficiency and robustness of the approach are illustrated on an example where the exponent in the power law is spatially dependent.

ABSTRACT In this paper, we propose an approximate analytical solution of the problem of nonlinear diffusion of the current density in a high-temperature superconducting plate with current transport. It is obtained by the technique of self-similar solution. The construction of this solution highlights a characteristic time of penetration Tp whose limit for large n is the model of Bean. We compare our solution to the ones obtained using COMSOL multiphysics. We study the influence of variation of the magnetic induction on time penetration and the influence of the n factor on time penetration.

ABSTRACT In this paper, we numerically study the influence of the speed variation of a magnetic source on the distribution of current density, magnetization, and dissipated energy of a high-temperature superconducting cylinder described by a Jn power law. The results presented come from the resolution of a nonlinear diffusion problem of electric field by a mixed finite-element finite-volume discretization method. This method is robust, stable, and converges for large values of n . The calculations carried out for n , varying from 1 to 200, show that when the external magnetic field quickly varies from 0 to its maximal value, the maximum values of penetration, the magnetization, and the energy dissipation are obtained when the switching of magnetic field occurs. For a periodic magnetic field, we note that any change of the period results in variation of the magnetization and the dissipated energy.

ABSTRACT In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded. The perfectly matched layer (PML) is widely used to simulate the truncation of the computational domain. However, its performance depends critically on an absorption function. This function is generally tuned by using case-dependent optimization procedures. In this paper, we will present some efficient functions that overcome any tuning. They will be compared using a realistic scattering benchmark solved with the Discontinuous Galerkin method.