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

Duke University, Durham NC

Investigators

Abstract

Proposal #0098140 Duke University Liu, Qing Huo In 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 characterize the 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 general layered 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). The collaborated 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.