Gakhov A. Discrete singularity method and computer tools for modelling of diffraction of acoustic waves on three-dimensional plane-parallel structures

The object is a process of acoustic waves diffraction in space on flatness structures. The goal is a development of the mathematical models and numerical methods based on discrete singularities method and development of the software for numerical experiments. Methods are method of parametric representation of integral and pseudodifferential operators, potential theory method, method of closed discrete vortex frames, methods of linear algebra, least squares method, the computational methods, the methods of structural and object-oriented programming, methods of quality standards. For the first time based on pseudodifferential equations the mathematical models have been created for problems of acoustic waves diffraction on a flat screen that is located on the plane between two media, over a rigid wall in a homogeneous space, on the layer over a rigid wall. The new pseudodifferential operators have been evolved and the kernels are investigated. For the first time the discrete model has been developed. The methods of computer verification of practical convergence of the discrete model solutions have been improved by adding the criteria that have physical meaning. For the first time the method has been built for checking the adequacy of computer-based approach to reduce the dimension of discrete model SLAE. The results are introduced in the educational process. Areas of use are education, environment, engineering.