本项目针对电磁散射问题，发展一种可靠的、高精度的谱元并行计算方法。首先, 考虑两层均匀介质和非均匀介质电磁波散射问题，利用边界积分方法处理索末菲辐射条件，将问题转换为带奇性积分边界条件的有界区域问题，再结合谱元法对问题进行求解，同时研究解的存在唯一性；对奇性积分，研究如何利用谱元法构造出高精度的积分格式；在上述研究的基础下，进一步研究如何建立中高波数电磁波散射问题的高精度谱元解法。 其次, 我们针对大尺度的电磁散射问题，提出新型的谱元并行算法，把大规模问题分成多个小规模问题分别在不同的处理器上同时进行数值模拟，拟重点解决计算过程中分块区域间数据的交换问题。 通过上述课题的研究，力争为实际科学计算中相关问题的解决提供行之有效的理论参考及数值求解方法。

This project will develope a reliable, high-precision parallel spectral element method based on MPI for electromagnetic scattering problems. Firstly, consider the two uniform and inhomogeneous media electromagnetic scattering problems, use the boundary integral method to deal with the Sommerfeld radiation condition, solve the problem by spectral element method by the problem with singularity integral boundary conditions bounded region, and investigate the existence and uniqueness of solutions; Construct a high-precision integration scheme by spectral element method for the singular integration; furthermore，propose a high-precision spectral element method for the electromagnetic wave scattering problems in high wave numbers. Secondly, we propose a new type of parallel spectral element algorithms for large-scale electromagnetic scattering problems. Large scale problem can be divided into a number of small-scale subproblems and we can simulate subproblems at the same time on different processors respectively. We intends to focus on resolving the calculation data commulations between the processors. By the study of this topics, we strive to provide an effective theory and numerical solution method in practical scientific computing applications.