Efficient solutions of wave propagation problems in multi-layered, multiple scattering media

该奖项支持首席研究员在各种应用环境中对波散射问题进行准确和有效的数值模拟的研究计划的延续。在这个项目中，首席研究员将开发和分析高性能、高效、准确和快速收敛的算法，用于评估涉及多个散射体以及具有不同材料特性的多层结构之间的波和结构之间的相互作用。待开发的求解器涉及多种应用，如雷达和遥感、通信设备、地球物理和光子学。首席研究员将开发一系列算法，主要集中在(1)层状介质中电磁和弹性散射问题的有效边界积分解决方案，绕过了对层状格林函数进行昂贵评估的需要；(2)多重散射问题的有效解决方案的Schur补域分解方法。所提出的工作的计算方法是基于近年来由首席研究员和他的合作者开发的一类数值求解器和表面表示和网格方法。这些是边界积分求解器，可以产生具有高阶精度的解，并且没有数值色散，适用于实际的工程几何形状，包括完整的飞机，复杂的光子或电子设备等特征。在实践中，无论何时适用，这些类型的求解器在给定的精度下，已经证明了比其他一些最具竞争力的求解器更快的数量级：新方法可以解决以前棘手的问题。

This award supports a continuation of the research program of the Principal Investigator on the accurate and efficient numerical modeling of wave-scattering problems in various applications settings. In this project, the Principal Investigator will develop and analyze high-performance, efficient, accurate, and rapidly-convergent algorithms for evaluation of the interaction between waves and structures that involve multiple scatterers as well as multiple layers with different material properties. The solvers to be developed are relevant to diverse applications, such as radar and remote sensing, communication devices, geophysics, and photonics.The Principal Investigator will develop a family of algorithms that will focus mainly on (1) efficient boundary integral solutions of electromagnetic and elastic scattering problems in layered media that bypass the need for cripplingly expensive evaluations of layered Green's functions and (2) Schur complement Domain Decomposition methods for efficient solutions of multiple scattering problems. The computational methodology underlying the proposed work is based on a class of numerical solvers and surface-representation and meshing methodologies developed in recent years by the Principal Investigator and his collaborators. These are boundary integral solvers that can produce solutions with high-order accuracy, and no numerical dispersion, for realistic engineering geometries including features such as full aircraft, complex photonic or electronic devices, etc. In practice, and whenever applicable, these types of solvers have demonstrated order-of-magnitude faster numerics, for a given accuracy, than some of the most competitive solvers otherwise available: the new methods can enable solution of previously intractable problems.