In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the SaintVenant system of shallow water equations wit...In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the SaintVenant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution展开更多
A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,whi...A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation.We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work.For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency,a continuation method is introduced to ensure the convergence of the iterative procedure.The convergence of our method is fast.Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges.The maximum total conversion efficiency available reaches more than 50%in all the cases studied.展开更多
In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of ach...In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of achieving high order accuracy and mesh efficiency. We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem. The computational results verify that, by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al., an order of N^-3/2 accuracy can be obtained when continuous piecewise linear elements are used, where N is the number of elements.展开更多
文摘In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the SaintVenant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution. The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution
基金supported by the fundamental research funds for the central universities(BUPT2009RC0706)the Project 11001030 supported by National Natural Science Foundation of China+3 种基金the open fund of key laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)of Ministry of Educationsupported in part by the NSF grants DMS-0604790,DMS-0908325,CCF-0830161,EAR-0724527,and DMS-0968360the ONR grant N00014-09-1-0384a special research grant from Zhejiang University.
文摘A computational study on the enhancement of the second harmonic generation(SHG)in one-dimensional(1D)photonic crystals is presented.The mathematical model is derived from a nonlinear system of Maxwell’s equations,which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation.We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work.For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency,a continuation method is introduced to ensure the convergence of the iterative procedure.The convergence of our method is fast.Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges.The maximum total conversion efficiency available reaches more than 50%in all the cases studied.
文摘In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of achieving high order accuracy and mesh efficiency. We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem. The computational results verify that, by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al., an order of N^-3/2 accuracy can be obtained when continuous piecewise linear elements are used, where N is the number of elements.
