Elastic Wave Scattering by Surface-Breaking Cracks and Cavities

摘要： 该项目的目的是开发实际有效的和理论上严格的解决方案，以广泛的技术问题，具体应用于非破坏性评估的问题，通过弹性波散射从表面破裂裂缝和结构中的空腔。在该方法中，波场表示通过辅助相位和振幅函数。相函数，也被称为“程函”，由动力学中的经典Hamilton-Jacobi方法确定。振幅函数由随机游走法确定，其系统使用是该项目的核心创新。该方法通过非常简单和明确的概率公式提供波场的描述。 拟议的工作预计将显着影响大多数领域处理复杂现象的建模连续。预计非破坏性评估、物理学、声学、雷达、电信技术等领域以及处理波传播的其他领域将特别受益于该项目。 这种相当大的影响是通过使用一种新的方法，结合了简单的渐近方法与直接数值方法的多功能性。所使用的方法与传统方法兼容，并且它采用具有低存储器要求和无限并行处理能力的可扩展算法。这是一种方法，是理想的计算设施的发展现状，依赖于理论的发展统计，自20世纪20年代以来发生的。

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.