Section: New Results
Numerical analysis and simulation of heterogeneous systems
Participant : Xavier Antoine.

In [10], we design some accurate artificial boundary conditions for the semidiscretized linear Schrödinger and heat equations in rectangular domains. We show the accuracy of the method thanks to simulations

In [5], we design fast numerical and highly accurate methods for the computation of steady states and the dynamics of time or spacefractional Schrödinger equations.

In [1], we design a numerical model of diffusion for the study of the properties of noble gases originating from volcanic eruptions.

In [4], the deal with a multilevel Schwarz Waveform Relaxation (SWR) Domain Decomposition Method (DDM) for the Non Linear Schrödinger Equation (NLSE).

In [6], we design a fast and pseudo spectral preconditioned conjugated gradient method for the computation of the steady states related to the GrossPitaevskii equation with non local dipolar interaction.

In [3], we deal with fractional microlocal analysis for the obtention of asymptotic estimates for the convergence of Schwarz Waveform Relaxation (SWR) domain decomposition method; this study is done is the two dimensional quantum case.

In [11], we design new methods of very high order for the computation of diffracted fields; these methods rely on a Bsplines finite element method and are related to the isogeometric analysis.

In [17], we deal with the numerical analysis of fast and accurate schemes for solving onedimensional timefractional nonlinear Schrödinger equations set with artificial boundaries.

In [35], we obtain a close approximation of the optimal parameters for the convergence of domain decomposition methods for the Schrödinger equation.

In [19], we compute an explicit approximation of the optimal parameters for the convergence of domain decomposition methods for the Schrödinger equation.

In [21], we introduce an original method in order to integrate PML in a pseudospectral method for the computation of the dynamics of the Dirac equation. Some applications to lasers are given.

In [20], we deal with the asymptotic analysis of the rate of convergence of the classical and quasioptimal Schwarz waveform relaxation (SWR) method for solving the linear Schrödinger equation.