中文摘要：

针对以全内反射显微镜为模型的近场散射问题提出一种超弱变分方法。在计算区域网格剖分的基础上，利用Green公式将问题转化到网格边界上求解，并利用平面波函数和倏逝波函数逼近解的局部性态。结果表明，算法能有效数值模拟近场散射问题，适用于大波数情形，收敛速度快。

英文摘要：

An ultra weak variational method was proposed for the time harmonic scattering problem in view of total internal reflection microscopy as a model.Based on the partition of the computational domain,the problem was transformed into the one on the skeleton of the mesh.By Green identity, the equivalent ultra weak variational formulation was deduced. Then plane wave functions and evanescent wave functions were used to approximate the local property of the solution.The method is suitable for the problems with big wave number,and has a fast rate of convergence,by which the scattering problem in near field can be effectively solved.