We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we dis...We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.展开更多
In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded domains.We present in detail the most recent approaches and describe briefly alternative...In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded domains.We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works.We conclude with several numerical examples from different application areas to compare the presented techniques.We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.展开更多
We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditi...We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.展开更多
基金This work is supported by Thales Alenia Space.We are gratefully indebted to J.-F.Coulombel,F.GolseK.Aoki for many useful advices concerning this work and for their kind encouragements。
文摘We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.
文摘In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded domains.We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works.We conclude with several numerical examples from different application areas to compare the presented techniques.We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.
基金supported by the French ANR fundings under the project MicroWave NT09_460489.
文摘We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.
