FAHS , Hassan

The paper discusses high-order geometrical mapping for handling curvilinear geometries in high-accuracy discontinuous Galerkin simulations for time-domain Maxwell problems. The proposed geometrical mapping is based on a quadratic representation of the curved boundary and on the adaptation of the nodal points inside each curved element. With...

This paper discusses isoparametric technique for handling curvilinear geometries in high accuracy discontinuous Galerkin (DG) simulations for time-domain Maxwell's equations. With isoparametric elements, numerical fluxes along curved boundaries are computed much more accurately due to the high-order representation of the computational domain....

A high-order leap-frog based non-dissipative discontinuous Galerkin time-domain method for solving Maxwell's equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a Nth-order leap-frog time scheme. Moreover, the interpolation...

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the...

This paper reviews the main features of a high-order non-dissipative discontinuous Galerkin (DG) method recently investigated in [H. Fahs, Int. J. Numer. Anal. Model., 6, 193-216, 2009] for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter...

We report on a detailed numerical evaluation of the non-dissipative, non-conforming discontinuous Galerkin (DG) method on triangular meshes, for solving the two-dimensional time-domain Maxwell equations. This DG method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with...

This work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the...

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell's equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a...

In this work, we discuss the formulation, stability, convergence and numerical validation of a high-order leap-frog based non-dissipative discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. This DGTD method makes use of a nodal polynomial interpolation method for the...

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the 2D time-domain Maxwell's equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of...

On étudie la stabilité d'une méthode Galerkin discontinu pour la résolution numérique des équations de Maxwell 2D en domaine temporel sur des maillages triangulaires non-conformes. Cette méthode combine l'utilisation d'une approximation centrée pour l'évaluation des flux aux interfaces entre éléments voisins du maillage, á un schéma...

We study numerically the pair trajectories of rigid circular particles in a two dimensional inertialess simple shear flow of a (Binghamian) yield stress fluid. We use a Lagrange multiplier based fictitious domain method, following Glowinski et al. [26, 28, 29], for solving the problem. Contacts between the particles at a finite interparticle...

This paper is concerned with the design of a high-order discontinuous Galerkin (DG) method for solving the 2-D time-domain Maxwell equations on nonconforming triangular meshes. The proposed DG method allows for using nonconforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of...

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Max\-well equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the...

We report on results concerning a discontinuous Galerkin time domain (DGTD) method for the solution of Maxwell equations. This DGTD method is formulated on unstructured simplicial meshes (triangles in 2-D and tetrahedra in 3-D). Within each mesh element, the electromagnetic field components are approximated by an arbitrarily high order nodal...

The great majority of numerical calculations of the specific absorption rate (SAR) induced in human tissues exposed to microwaves are performed using the finite difference time-domain (FDTD) method and voxel-based geometrical models. The straightforward implementation of the method and its computational efficiency are among the main reasons for...