Collaborative Research: Parallel Hybrid Differential and Integral Equation Based Solvers for Time Domain Electromagnetic Analysis with Application to High-Speed Circuits

该项目的目标是开发面向高速电路应用的快速准确的基于物理的并行瞬变电磁解算器。这是通过高性能并行算法的组合，允许分层计算的数值方案的新进展，最后，不同的数值技术的杂交。更具体地说，正在追求以下目标：（一）发展新的数值方案，减少总的计算工作和相应的并行方案;（二）发展并行和数值方法，用于分析瞬态场的扩散和色散材料介质;（三）开发用于集成基于微分方程和积分方程的方案的并行方法，使得可以获得优势两者，（iv）最后，将上一项中开发的EM求解器集成到电路仿真工具SPICE中，以实现电路的全波EM仿真。所提出的研究的主要影响是高性能瞬态电磁分析工具，适用于各种设计和分析问题的发展。所开发的技术被用于分析高速电路中的问题，包括片上信号完整性、非线性器件、串扰、反射和非线性终端。电磁（EM）现象构成了从电气到电子到通信到计算机技术的应用的物理基础，并且完全由麦克斯韦方程描述。快速准确的基于物理的仿真工具为电磁现象的研究提供了第二种模式，并且在民用和军用研发环境中迅速成为不可或缺的。作为这一奋进的一部分，密歇根州立大学和爱荷华州州立大学的研究人员正在合作开发一个快速准确的仿真工具库，这些工具允许进行动态优化，可用于电磁设备的快速设计原型。为此，正在开发用于瞬变电磁分析的新的数值方法和并行化这些方法的算法。所开发的技术正在应用于电磁器件的设计和分析。

The goal of this project is to develop fast and accurate physics-based parallel transient electromagnetic solvers that are geared towards applications to high-speed circuits. This is being achieved via a combination of high performance parallel algorithms, novel advances in numerical schemes that permit hierarchical computation and finally, the hybridization of different numerical techniques. More specifically, the following objectives are being pursued: (i) development of novel numerical schemes that reduce the overall computational work and the corresponding parallel schemes; (ii) development of parallel and numerical methods for analyzing transient fields in diffusive and dispersive material media; (iii) development of parallel methodologies for integrating differential equation and integral equation based schemes such that one can reap the advantages of both; (iv) and finally, integrating the EM solver developed in the last item into the circuit simulation tool SPICE, to enable fullwave EM simulation of circuits. The principal impact of the proposed research is the development of high performance transient electromagnetic analysis tools that are applicable to a variety of design and analysis problems. The techniques developed are being used to analyze issues in high-speed circuits including on-chip signal integrity, non-linear devices, cross-talk, reflections, and non-linear terminations.Electromagnetic (EM) phenomena constitute the physical underpinnings of applications ranging from electrical to electronic to communication to computer technologies and are completely described by Maxwell's equations. Fast and accurate physics-based simulation tools offer a second modality of investigation into electromagnetic phenomena, and are rapidly becoming indispensable in civilian and military R & D settings. As a part of this endeavor, researchers at Michigan State University and Iowa State University are collaborating on developing an arsenal of fast and accurate simulation tools that permit on-the-fly optimization that can be used for rapid design prototyping of electromagnetic devices. To this end, novel numerical methods for transient electromagnetic analysis and algorithms to parallelize these are being developed. The techniques developed are being applied to the design and analysis of electromagnetic devices.