Abelin Kameni

Multirate Technique for Explicit Discontinuous Galerkin Computations of Time-Domain Maxwell Equations on Complex Geometries

This paper presents a multirate technique to improve and optimize the time step of a second-order two-stage explicit Runge-Kutta (ERK) scheme. In this technique, the mesh elements are stored in different groups according to their stable time steps. These groups are sorted into two classes: 1) the bulk groups, where the two-stage ERK method is applied once or repeatedly; 2) the buffer groups that are used to accommodate the transition between two bulk groups. This technique is proposed for accelerating the explicit discontinuous Galerkin computations of the time-domain Maxwell equations. An application example on a human skull is proposed to show the efficiency of this technique and to simulate wave propagation on complex geometries.

3-D Equivalent Model to Compute the Electro-Magnetic Behavior of Twisted Multi-Filamentary Superconductors Wires

In this paper, we investigate new methods to model in 3-D, efficiently and simply, twisted multi-filamentary superconductors subjected to an external magnetic field. Several simulation cases, based on the H-formulation implemented in GetDP, will help derive through appropriate methods, such as changing the reference from where the problem is seen and described to a reference where everything becomes simple to deal with, a simple equivalent 3-D problem to solve efficiently and quickly.

H-Formulation Using the Discontinuous Galerkin Method for the 3-D Modeling of Superconductors

In this paper, a new approach to model efficiently high-temperature superconductors, whose electrical behavior is characterized by a non-linear power law, in 3-D is investigated. The commonly used non-linear H-formulation will be discretized based on the discontinuous Galerkin method. This numerical approach will likely provide fast simulations through parallel computations. Its application on simple examples, such as a superconducting cube subjected to an external magnetic field, will show robustness, convergence, and fast computations.