In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transp...In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.展开更多
We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that ti...We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that tile data of the upstream flow and the pressure at downstream part jointly determine the whole flow, as well a the wave structure. Particularly, we show that the height of the Mach stem depends not only on the data of upstream flow, but also on the pressure at downstream flow. The flow with the assigned wave structure is governed by a free boundary value problem for the Euler system. In the problem the location of the triple point, the shock fronts and the contact discontinuity are all unknown, they are finally determined together with the solution.展开更多
基金supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Project No.CityU 102204).
文摘In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.
基金supported by National Natural Science Foundation of China(Grant Nos.11031001 and 11101101)
文摘We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that tile data of the upstream flow and the pressure at downstream part jointly determine the whole flow, as well a the wave structure. Particularly, we show that the height of the Mach stem depends not only on the data of upstream flow, but also on the pressure at downstream flow. The flow with the assigned wave structure is governed by a free boundary value problem for the Euler system. In the problem the location of the triple point, the shock fronts and the contact discontinuity are all unknown, they are finally determined together with the solution.
