本项目旨在完善电磁波时程精细积分法的基础理论体系，着重于影响方法的计算精度、计算速度和稳定性的各种因素研究，达到能有效地降低方法对计算机资源需求，使其成为一种实用化电磁场时域计算方法之目的。所涉及的研究内容主要有：在理论上揭示吸收边界条件引入对算法数值稳定性和数值色散特性影响的数学物理本质；构造适用于复杂媒质（各向异性、色散、非线性）电磁波时程精细积分法的算法；发展电磁波时程精细积分法与其他数值方法相结合的混合算法；研究电磁波时程精细积分法应用中的子域技术和并行化计算策略。这些研究工作不仅能够改观目前电磁波时程精细积分法的理论研究和实际应用现状，有着非常重要的学术意义，而且也符合计算电磁学的发展趋势（主要体现在对各种快速算法的研究上），可望使电磁场时域计算能力得到明显改善，对推动计算电磁学发展具有重要的作用。

In this project, the basic theory of the precise-integration time-domain (PITD) method for electromagnetic wave will be improved, and the fundamental issues is to study the various relevant factors influencing the computational accuracy, the computational speed and the numerical stability of the PITD method, so as to effectively reduce the demand for computer resources and make the PITD method become a kind of practical time-domain calculation method of electromagnetic field. The main research contents involved are: to reveal the mathematical and physical nature of absorbing boundary conditions into the influence on the numerical stability and the dispersion properties of the algorithm in theory, to construct and analyze the precise-integration time-domain method for complex medium (anisotropy, dispersion and nonlinearity) theoretically, to develop the hybrid algorithms which combine the precise-integration time-domain method and other numerical methods, and to study the parallel computing strategy for the precise-integration time-domain method. These researches can not only upgrade the current theoretical research and practical application of the precise-integration time-domain method for electromagnetic wave, but also conform to the development tendency of the computational electromagnetics (mainly reflected in the research of various fast algorithms). Thus, these studies are of very important significance for the academic research, and can improve the capacity of the time-domain calculation for electromagnetic field obviously, and will make great contributions to the development of computational electromagnetics.