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.