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快速和准确的基于物理的并行瞬变电磁解算器，适用于高速电路的应用。这是通过高性能并行算法、允许分层计算的数值格式的新进展以及不同数值技术的混合来实现的。更具体地说，正在追求以下目标：(I)开发减少总计算量的新型数值格式和相应的并行格式；(Ii)开发用于分析扩散和色散材料介质中的瞬变场的并行和数值方法；(Iii)开发用于集成基于微分方程和积分方程的格式的并行方法，以便人们能够获得两者的优点；(Iv)以及最后，将在最后一项中开发的EM求解器集成到电路模拟工具SPICE中，以实现电路的全波EM模拟。拟议研究的主要影响是开发适用于各种设计和分析问题的高性能瞬变电磁分析工具。开发的技术被用来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、从通信到计算机技术的各种应用的物理基础，并完全由麦克斯韦方程描述。快速和准确的基于物理的模拟工具为研究电磁现象提供了第二种方式，并正在迅速成为民用和军事研发环境中不可或缺的工具。作为这项努力的一部分，密歇根州立大学和爱荷华州立大学的研究人员正在合作开发一系列快速而准确的模拟工具，这些工具可以进行即时优化，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算法。所开发的技术正被应用于电磁设备的设计和分析。

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.