Phase Space Methods and Path Integration: A Microscopic Approach to Direct and Inverse Wave Propagation

摘要

This project focuses on the development of new, multidimensional algorithms for direct acoustic propagation and generalized acoustic tomography at the level of the scalar Helmholtz equation. The general aim is the continued detailed development of the ideas originally outlined several years ago. phase space, or microscopic, methods and path (functional) integral representations provide the appropriate framework to extend homogeneous Fourier methods to inhomogeneous environments. The path integrals furnish the principal representation of the Helmholtz propagator and, subsequently, through direct computation, the basis for the direct numerical algorithms. There are two complementary approaches to the analysis and computation of the n-dimensional Helmholtz propagator.