High Order Numerical Method For Scattering Problem With Elongated Scatterer

This paper mainly investigates the high order numerical method for scat?tering problem with elongated scatterer.By combining the spectral elemen-t method with the elliptical artificial boundary and the corresponding exact nonreflectiing boundary condition,a high order numerical method is obtained.Since the scatterer is elongated,truncation by circular artificial boundary shall result large computational domain hence more computation cost.Therefore,this paper adopts the elliptical artificial boundary,to make the artificial bound-ary can be very close to the scatterer.Then the size of the computational domain is reduced.Due to the fact that the exact nonreflecting boundary con-dition involves the Mathieu expansion coefficient of the unknown function,it is a global boundary condition.In order to obtain high accuracy,we propose an semi-analytic scheme for the calculation of the integral term on the artificial boundy.A large number of numerical experiments show that the numerical method presented in this paper has spectral accuracy.