针对复杂多物理电磁环境的新型宽带区域分解算法

High performance computing and the rising cloud computing are pushing computational electromagnetics (CEM), a critical technology for many engineering and scientific applications, to migrate to domain decomposition methods (DDM) so that the distributed systems can be used to expand our complex computational capability. .To properly handle open space problems and long mutual coupling distances problems, such as broadband stealthy aircrafts, complex antenna systems, photonic band gap structures, and IC interconnects, integral equation (IE) based DDM methods are necessary to be developed. ..However, the broadband IE based DDMs were seldom investigated. At low frequencies, the circuit theory will dominate; at mid frequencies, the wave propagation theory will dominate. Hence, to handle the broadband computation properly, we must contain both physics into the same solver. Because of the scale of today's problems, the broadband multi-physics IE DDM is increasingly important but it was seldomaddressed in literatures. ..To establish a broadband CEM solving algorithm, it requires a broadband physical model and a broadband numerical acceleration engine. In this proposal, we will develop both of them in one novel IE based domain decomposition schemeto solve the band limitation in computing large-scale multi-physics problems...It has following distinct technological features: ..(1).A complete broadband solution containing both low frequency physics and mid frequency physics: the proposed method not only provides the broadband physical model, but also the broadband numerical acceleration engine. Hence it provides a complete solution. ..(2).Novel equivalence principle algorithm using both charges and currents: by introducing charge terms on equivalence surfaces, the new augmented equivalence principle algorithm will be completely loop-tree free at low frequencies. It will be further integrated with the mid frequency equivalence principle algorithm dynamically to serve as the broadband physical model...(3).Rotated mixed-form fast multipole algorithm (R-MFFMA): we will use the pseudospectral projection to rotate spherical harmonic functions so that the multipole truncation number could be very large to move the multipole-plane wave transition position of mixed-forma FMA (MF-FMA) to higher frequencies.Hence, the overall reliability, efficiency, and accuracy of R-MFFMA can be significantly improved relative to MF-FMA to serve as a better broadband numerical engine...This novel CEM method provides a complete DDM solution including both novel broadband physical model (IE DDM) and novel broadband numerical engine (R-MFFMA). It fills the voids of IE DDM and can serve as a general computational electromagnetics framework to solve multi-band antenna arrays, broadband radar scattering, photonic band gap structures, and complex EMC/EMI problems, etc.

高性能计算和云计算使计算电磁学正向区域分解方法发展。基于积分方程的宽带区域分解法十分重要，但文献中尚少研究。因低频和中频电磁场的物理差异很大，为解决宽带，必须同时处理两种物理机制。而且物理模型和数值加速引擎都必须宽带。..本项目将基于积分方程建立宽带区域分解框架,有如下创新点：.1..涵盖低频和高频物理的完整算法：.不仅有宽带物理模型，而且有宽带数值加速引擎。从而提供一个完整方案。.2..使用等效电／磁流和等效电／磁荷的新等效原理方法：.开发增强型等效面算法（A-EPA）处理低频，避免 Loop-Tree 基函数。.3..旋转混合型快速多极子算法（R-MFFMA）：.使用伪谱投影方法旋转处理低频多极子，保证多极子截取数目数百的精度和速度，提升混合型快速多极子算法的转换频率，保证宽带数值加速的可靠性，效率和精度。..本方法可应用于宽带隐身飞行器，复杂天线系统，光学晶体，和复杂电磁兼容等方面.

由于复杂电磁应用的建模需求，基于积分方程的宽带区域分解方法面临巨大挑战。因低频和中频电磁场的物理差异很大，我们致力于解决宽带电磁模型的建立和宽带数值加速引擎的开发。 ..通过专注研发以及与国内外一流学者的合作，我们在本课题的执行和研发过程当中取得了多项重要原创性研究成果，并且取得多项国际学术奖的认可。我们研究的主要内容，重点成果，及其关键科学意义包括：..1..进行了一系列低频积分方程的算法研究， 率先提出了如基于库仑规则的新型低频积分方程方法。 这些工作为我们宽带电磁计算奠定理论和方法基础。..2..提出并且开发了宽带增强型等效面算法（A-EPA），通过使用表面等效电流和等效电荷，以及A-EFIE算子，我们不仅提供了宽带区域分解计算框架，而且避免复杂的Loop-Tree 基函数的使用。..3..提出并开发了新型分层松弛型等效面方法 （RHESA），根本上消除了传统矩形等效面的不连续性，避免了Tap 基函数的使用和相关奇异性，实现了物理模型上的分层区域分解的高精度快速计算。..4..成功开发了新型旋转型混合快速多极子算法 (MF-FMA)， 实现了低频部分对角化，从而上移MF-FMA的转换区间，为大型宽带电磁计算提供精度可控的宽带引擎。..5..率先解决了DGTD和IE结合的区域分解算法，成功实现了DGTD共形边界的计算问题，解决了通过时域进行宽带和非线性的区域分解计算问题。..6..拓展了传统的积分方程方法的线性前提局限，开发了新型宽带纳米非线性材料PMCHWT积分方程方法。并以此为独特工具，首创了非线性八木纳米天线, 实现了基于频谱的空域区分。..7..为解决有限周期结构的大规模计算问题，提出了基于表面波指数衰减特性和周期结构Bloch-Floquet模式的快速计算方法，成功重构了有限周期结构的周期波和表面波，避免了大量阵单元的耦合计算。..本课题的工作对宽带电磁计算方法提供了原创性的新贡献。所研发的计算方法可以被广泛应用于宽带隐身技术，复杂天线系统，纳米光学系统，和复杂电磁兼容等方面。本课题组的科研努力已经获得多项国际会议大奖的认可。