In this article we aim at proposing a general mathematical formulation for charge conserving finite element Maxwell solvers coupled with particle schemes. In particular, we identify the finite element continuity equations that must be satisfied by the discrete current sources for several classes of time domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in 2 or 3 dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high order charge conserving FEM-PIC numerical schemes.

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This paper is dedicated to recent developments of a two-Lagrange multipliers domain decomposition method for the Helmholtz equation [C. Farhat et al., an additional augmented operator along the interface between the subdomains. Most methods for optimizing the augmented interface operator are based on the discretization of approximations of the continuous transparent operator [B. At the discrete level, the optimal operator can be proved to be equal to the Schur complement of the outer domain. This Schur complement can be directly approximated using purely algebraic techniques like sparse approximate inverse methods or incomplete factorization. The main advantage of such an algebraic approach is that it is much easier to implement in existing code without any information on the geometry of the interface and the finite element formulation used. Convergence results and parallel efficiency of several algebraic optimization techniques of an interface operator for acoustic analysis applications will be presented.

Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta scheme. We also construct in a systematic way a high-order quadrature which is optimal in terms of the number of points, which enables the use of mass lumping, up to P 5 elements. We compare computational time and effort for several codes which are of high order in time and space and study their respective properties.

The framework provides a versatile and reusable tool for the simulation of any MRI experiment including physiological fluids and arbitrarily complex flow motion.

We describe the efficient algebraic reconstruction (EAR) method, which applies to cone-beam tomographic reconstruction problems with a circular symmetry. Three independant steps/stages are presented, which use two symmetries and a factorization of the point spread functions (PSFs), each reducing computing times and eventually storage in memory or hard drive. In the case of pinhole single photon emission computed tomography (SPECT), we show how the EAR method can incorporate most of the physical and geometrical effects which change the PSF compared to the Dirac function assumed in analytical methods, thus showing improvements on reconstructed images. We also compare results obtained by the EAR method with a cubic grid implementation of an algebraic method and modeling of the PSF and we show that there is no significant loss of quality, despite the use of a noncubic grid for voxels in the EAR method. Data from a phantom, reconstructed with the EAR method, demonstrate 1.08-mm spatial tomographic resolution despite the use of a 1.5-mm pinhole SPECT device and several applications in rat and mouse imaging are shown. Finally, we discuss the conditions of application of the method when symmetries are broken, by considering the different parameters of the calibration and nonsymmetric physical effects such as attenuation.

We consider a system of two reaction-dispersion equations with nonconstant parameters. Both equations are coupled through the boundary conditions. We propose a mixed variational formulation that leads to a nonsymmetric saddle-point problem. We prove its well-posedness. Then, we develop a stabilized mixed finite element discretization of this problem and establish optimal a priori error estimates.