Elastic Wave Scattering by Surface-Breaking Cracks and Cavities

摘要：该项目旨在为广泛的技术问题开发实用有效和理论严谨的解决方案，并具体应用于结构表面破裂裂纹和空洞的弹性波散射无损评估问题。在该方法中，波场用辅助的相位和幅度函数来表示。相函数，也被称为“eikonal”，由动力学中的经典哈密顿-雅可比方法确定。幅值函数的确定采用随机游动法，其系统化使用是本项目的核心创新。这种方法用非常简单和明确的概率公式来描述波场。这项拟议的工作预计将对处理连续介质中复杂现象的建模的大多数领域产生重大影响。无损评估、地球物理、声学、雷达、电信技术和其他与波传播有关的领域预计将特别受益于该项目。这种巨大的影响是通过使用一种新的方法来提供的，该方法结合了渐近方法的简单性和直接数值方法的多功能性。该方法与传统方法兼容，并采用内存需求低、并行处理能力不受限制的可扩展算法。这是一种理想的方法，适用于目前计算设施的发展状况，依赖于自1920年S以来发生的统计学理论发展。

Abstract: The project is intended to develop practically efficient and theoretically rigorous solutions to a broad class of problems in technology with specific applications to problems in non-destructive evaluation by elastic wave scattering from surface breaking cracks and cavities in structures. In the method, wave fields are represented through auxiliary phase and amplitude functions. The phase function, known also as the "eikonal", is determined by the classical Hamilton-Jacobi method in dynamics. The amplitude function is determined by the random walk method whose systematic use is the core innovation of the project. This method provides the description of the wave fields by extremely simple and explicit probabilistic formulas. The proposed work is expected to significantly affect most areas dealing with the modeling of complicated phenomena in continua. Such areas as non-destructive evaluation, geophysics, acoustics, radar, telecommunication technologies, and other areas dealing with wave propagation are expected to especially benefit from the project. Such considerable impact is provided by the use of a novel approach that combines the simplicity of asymptotic methods with the versatility of direct numerical methods. The method to be utilized is compatible with conventional methods, and it employs scalable algorithms with low memory requirements and with unlimited capability for parallel processing. It is an approach that is ideal for the present state of development of computational facilities, relying on theoretical developments in statistics that have occurred since the 1920's.