Seminar “Modeling of the wave perturbation propagation in the heterogeneous environment using the grid-characteristic method”

On 19 September at 12:00 p.m. (Moscow time)

This work is devoted to the development of numerical methods of higher order of accuracy and a software package for mathematical modeling of dynamic wave disturbances as applied to seismic, seismic exploration, geophysics, strength and nondestructive testing problems.

The main features of the developed methods are high accuracy and explicit separation of inhomogeneities in media. The sizes of computational areas in real geophysics problems reach tens of kilometers, while the sizes of inhomogeneities can reach units of meters and less. Such long-time problems require the use of high-precision numerical methods to correctly describe the propagation of dynamic wave perturbations in three-dimensional elastic formulation over large distances. Part of the work is devoted to the development of such methods.

Mesh-characteristic methods up to the fourth order of accuracy and bicompact mesh-characteristic schemes of the second to third order of accuracy have been developed and implemented as a software package. In addition, algorithms for explicit separation of media interfaces with an exact solution in the contact region were realized. Models of fractured heterogeneities with explicit separation of fracture boundaries have been developed. In case of solving heterogeneous kind of problems, an algorithm using hierarchical computational meshes has been developed and implemented. Parallel versions of the numerical methods were developed to ensure acceptable computation time. Parallel algorithms have been developed for all major architectures of modern high-performance supercomputers.

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