Fast Algorithms for Wave Scattering in Layered Media for Electronic Packaging and Geophysical Exploration

提案#0098140杜克大学Liu，Qing Huo在这个跨学科的项目中，我们建议开发分层介质中电磁波和弹性波散射的快速算法。这种共同努力的动力是对电子封装和地球物理勘探的有效和准确的数值模拟工具的需求不断增长，其中波现象在设计，评估，预测和生产中起着重要作用。在这两种应用中，迫切需要快速求解层状介质中全波方程的技术，即用于电子封装的麦克斯韦方程和用于地球物理勘探的电磁波和弹性波方程。 由于这两个波动方程的解所涉及的数值问题具有许多共同的特征，因此开发层状介质中波散射的快速算法将对这两个领域产生重大影响。在高速电子封装中，互连是系统速度性能的决定因素之一。 这样的高阶效应不容易在等式或表格中捕获，使得传统的定时驱动布局技术不准确和过时。 必须充分表征互连结构，以确保片上信号的完整性，并实现预期的高速系统性能。 因此，迫切需要更快、更精确的全波电磁分析工具来提取电阻、电容、电感等寄生参数。另一方面，在油气地球物理勘探中，电磁和声学传感器被广泛用于探测复杂地质构造。电磁和声学地下感测的目标是从这些测量中推断地层的电磁和机械性质，并且将联合收割机与诸如核的其它测量组合以确定储层的岩石物理特性。然而，由于地震波与复杂的地质构造和井眼的相互作用，这些地震波的解释仍然是一个具有挑战性的问题。 这些测量的解释和处理依赖于快速和准确的电磁波和声波在大规模的，高度不均匀的mediation.The主要重点的电磁波和弹性波传播的层状介质中的直接问题的数值算法的发展，该建议的正逆解。将使用频域积分方程公式。 主要工作包括：一般层状介质并矢绿色函数的快速计算，矩阵-向量乘法的快速实现和矩阵解算器的鲁棒预条件子，大目标高阶基函数的构造和研究，大目标高阶基函数的构造和研究。所获得的数值算法在电子封装和地球物理勘探中的应用。两位PI在建议的应用领域-VLSI和RF元件设计的参数提取方面有着丰富的经验（Cai）和地球物理地下传感和电子封装（Liu）。 这项合作研究将极大地有利于电子和石油勘探工业，以及我们在电气工程和应用数学和科学计算方面的研究和教育计划。

Proposal #0098140Duke UniversityLiu, Qing HuoIn this interdisciplinary project, we propose to develop fast algorithms for electromagnetic and elastic wave scattering in layered media. The impetus for such a joint effort is the ever increasing demand for efficient and accurate numerical simulation tools for electronic packaging and geophysical exploration where wave phenomenon plays an important role for design, evaluation, prediction and production. In both applications, there is a pressing need for fast solution techniques for full wave equations in layered media, namely, Maxwell's equations for electronic packaging and both electromagnetic and elastic wave equations for geophysical exploration. As the numerical issues involved in the solution of both wave equations share many common features, a concerted effort to develop fast algorithms for wave scattering in layered media will have a significant impact in both areas.In a high-speed electronic package, interconnects are one of the determining factors for the speed performance of the system. Such a high order effect is not easily captured in either equations or tables, rendering conventional timing driven layout techniques inaccurate and obsolete. One must fully characterizethe interconnect structures to ensure on-chip signal integrity and to achieve the expected high-speed system performance. Therefore, there is a strong need for faster and more accurate full-wave electromagnetic analysis tools to extract parasitic parameters such as resistance, capacitance, and inductance.On the other hand, in geophysical exploration for oil and gas, electromagnetic and acoustic sensors are widely used to probe complex geologic structures. The goal of electromagnetic and acoustic subsurface sensing is to infer from these measurements the electromagnetic and mechanical properties of the formation,and to combine with other, such as nuclear, measurements to determine the petrophysical characteristics of the reservoir. The interpretation of these easurements, however, remains a challenging problem because of the complicated interaction of waves with the complex geologic structures and wellbore. The interpretation and processing of these measurements depend on fast and accurate forward and inverse solutions of lectromagnetic and acoustic waves in large-scale, highly heterogeneous media.The main emphasis of this proposal is on numerical algorithm development relevant to direct problems for electromagnetic and elastic waves propagation in layered media. A frequency domain integral equation formulation will be used. Major tasks include fast calculation of dyadic Green's functions for generallayered media; fast matrix-vector multiplication and robust preconditioner for matrix solver; construction and study of high order basis functions for large targets; application of the obtained numerical algorithms in electronic packaging and geophysical exploration.Both PI's have extensive experience in the proposed application areas---parameter extraction for VLSI and RF component design (Cai) and geophysical subsurface sensing and electronic packaging (Liu). Thecollaborated research will greatly benefit the electronics and oil exploration industry, and our research and educational programs in electrical engineering and applied mathematics and scientific computation.