Advanced Computational Research in Electromagnetic Wave Interactions

当代高频电磁工程问题可能涉及全矢量波与复杂的、电大的三维结构的相互作用。这种结构的麦克斯韦方程组的数值模拟是非常重要的，因为经典的电动力学分析工具不能处理几乎任意复杂的矢量近场。当代数值模拟这类问题的两个主要方向是：(1)用矩量法求解的频域积分微分方程方法（MON）；(2)时域偏微分方程方法，用时域有限差分（FD-TD）方法求解。本研究项目将为最新版本的MOM和FD-TD开发连接机（CM）软件，构建相对于基于crays的版本的基准测试，并为超大型近场数据库的CM处理制定缩放规则。该项目还将把一种新的空间分解（SD）技术扩展到最新的组合场表面积分方程版本的MOM。SD在降低大型MOM问题的维数和不良条件方面非常有前途，并且可能允许现有计算机处理非常大的EM模型。

Contemporary high-frequency electromagnetic engineering problems can involve full-vector wave interactions with complex, electrically-large, three-dimensional structures. Numerical simulation of Maxwell's equations for such structures is of great importance since the classical analytical tools for electrodynamics cannot deal with vector near fields that may be almost arbitrarily complex. Two of the primary contemporary thrusts in numerically modeling such problems are: (1) the frequency-domain integro-differential equation approach with solution via the method of moments (MON); and (2) the time-domain partial differential equation approach with solution via the finite-difference time-domain (FD-TD) method. This research project will develop Connection Machine (CM) software for the latest versions of MOM and FD-TD, construct benchmarks relative to Cray-based versions, and develop scaling rules for CM processing of ultra-large near-field data bases. This project will also extend a new spatial decomposition (SD) technique to the latest combined-field surface integral equation versions of MOM. SD is very promising for reducing the dimensionality and ill-conditioning of large MOM problems, and may permit existing computers to process very large EM models.