中文摘要：

研究了用于求解电磁散射问题的WENO重构时域无网格算法。基于无网格点云结构,引入沿点云中心点和卫星点连线方向的局部一维坐标,并结合虚拟点的设置,构成在点云中实施三阶WENO重构所要求的模板,以便利用WENO重构计算中心点与卫星点连线中点处物理量的左右状态值,供通量运算。设置的虚拟点上的物理量则利用点云中已有的最近点插值系数直接插值确定。用发展的算法对典型的一维和二维电磁散射问题进行数值模拟,并与理论解和传统的基于线性重构的计算结果进行比较,验证了WENO重构获得的数值解比线性重构更接近理论解。给出了多体干扰电磁散射场算例,展示出用发展的算法处理复杂多体干扰情形的效果。

英文摘要：

A meshless time-domain algorithm based on weighted essentially non-oscillatory（WENO） reconstruction for solving the electromagnetic scattering problems is studied. The stencil required for implementing third-order WENO reconstruction in the gridless cloud is obtained by setting a local coordinate in the direction of each satellite point and introducing a virtual point so as to use WENO reconstruction to approximate the physical quantities at the midpoint between the central and satellite points of the gridless cloud. Additionally, physical quantities at the virtual point are determined by direct interpolation based on available interpolation coefficients of the nearest point. Then, approximate Riemann solver is introduced in dealing with the computation of the flux related to the governing equations, and an explicit four-stage Runge-Kutta scheme is employed in time-marching. After that, based on the developed algorithm, typical 1-D and 2-D cases for solving the electromagnetic fields are simulated. The simulation results verify that the numerical results calculated by using WENO reconstruction are closer to the theoretical solutions than that based on linear function reconstruction. The paper ends with the presentation of the electromagnetic scattering fields with multi-bodies, which show the developed algorithm has the ability to accommodate complex geometries.