The seminar on system programming under the supervision of A.I. Avetisyan on the topic: “Modeling the propagation of dynamic wave disturbances in heterogeneous media on high-performance computing systems” – was held on 25 June 2020 online, based on the Zoom platform.
Khokhlov Nikolay Igorevich, Ph.D., Head of the Department of Informatics and Computational Mathematics, Moscow Institute of Physics and Technology (MIPT), Senior Researcher, Deputy Head of the Laboratory of Applied Computational Geophysics, MIPT.
The work is devoted to the development of higher accuracy numerical methods and a software package for numerical modeling of dynamic wave disturbances as applied to seismic, geophysics, strength problems, and non-destructive testing problems. The main features of the developed methods are high accuracy and the explicit identification of inhomogeneities in the media. The dimensions of the computational domains in real geophysical problems reach tens of kilometers, while the size of heterogeneities can reach units of meters or less. In such long-time problems, the use of high-precision numerical methods is required to correctly describe the propagation of dynamic wave disturbances in a three-dimensional elastic formulation over long distances. Part of the work is devoted to the development of such methods. Mesh-characteristic methods up to the fourth-order of accuracy and compact mesh-characteristic schemes of the second-third order of accuracy were developed and implemented as a software package. In addition, algorithms for explicitly distinguishing media interfaces with an exact solution in the contact area were implemented. Models of fractured inhomogeneities with explicit identification of crack boundaries have been developed. In the case of solving various types of problems, an algorithm was developed and implemented using hierarchical computational grids. To ensure an acceptable simulation time, parallel versions of numerical methods have been developed. Parallel algorithms are designed for all major architectures of modern high-performance supercomputers.