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The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...
In this paper, we consider linear ordinary differential equations originating in
electronic engineering, which exhibit exceedingly rapid
oscillation. Moreover, the oscillation model is completely different
from the familiar framework of asymptotic analysis of highly
oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into
asymptotic series, and this allows us to extend Filon-type approach
to this setting. The outcome is a time-stepping method that guarantees
...
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
In this work, we investigate the Perfectly
Matched Layers (PML)
introduced by Bérenger [3] for designing
efficient numerical absorbing
layers in electromagnetism.
We make a mathematical analysis of this model, first via a modal
analysis with standard Fourier techniques, then via energy
techniques. We obtain uniform in time stability results (that make
precise some results known in the literature) and state some energy
decay results that illustrate the absorbing properties of the
model. This...
This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes...
We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the...
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