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

建议#0098140杜克大学刘庆火在这个跨学科的项目中，我们建议开发层状介质中电磁波和弹性波散射的快速算法。推动这种联合努力的是对用于电子封装和地球物理勘探的高效和准确的数值模拟工具的日益增长的需求，在这些领域，波现象在设计、评估、预测和生产中发挥着重要作用。在这两种应用中，迫切需要层状介质中全波方程的快速求解技术，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数值问题有许多共同的特点，共同努力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，互连是决定系统速度性能的因素之一。这样的高阶效应在方程式或表格中都不容易捕捉，使得传统的时序驱动布局技术不准确和过时。必须充分描述互连结构，以确保片上信号完整性并实现预期的高速系统性能。因此，迫切需要更快、更准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，在石油和天然气的地球物理勘探中，电磁和声波传感器被广泛用于探测复杂的地质构造。电磁和声地下传感的目的是从这些测量中推断地层的电磁和机械特性，并与其他测量相结合，如核测量，以确定储层的岩石物理特征。然而，由于波与复杂的地质结构和井筒的复杂相互作用，这些测量的解释仍然是一个具有挑战性的问题。这些测量数据的解释和处理依赖于大规模、高度非均匀介质中电磁波和声波的快速而准确的正解和反解。该建议的主要重点是与层状介质中电磁波和弹性波传播的正问题相关的数值算法开发。将使用频域积分方程式。主要任务包括：通用层状介质并矢格林函数的快速计算；矩阵求解器的快速矩阵-矢量乘法和稳健的预条件算子；大型目标的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。这两个PI在拟议的应用领域-超大规模集成电路和射频元件设计的参数提取(CAI)和地球物理地下传感和电子封装(LU)--都有丰富的经验。合作研究将极大地惠及电子和石油勘探行业，以及我们在电气工程、应用数学和科学计算方面的研究和教育项目。

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.