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
This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual ...This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.展开更多
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
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Project supported by the Fundamental Research Funds for the Central Universities (No. 2009B27514)the National Natural Science Foundation of China (No. 10871059)
文摘This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.
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.
