Varygina M.P.  

Numerical Modeling of Dynamic Interactions of Elastic Blocks and Thin Viscoelastic Interlayers with High-Performance Computations

Parallel computational algorithms for the numerical modeling of dynamic interactions of elastic blocks through thin elastic and viscoelastic interlayers in structurally inhomogeneous media such as rock are developed. Blocks are connected to each other with thin interlayers of rock with significantly weaker mechanical properties. Analysis of experimental data of wave propagation in layered media shows that the interlayers behave non-elastically even under small wave amplitudes. Models of deformation of  interlayer material of various levels of  complexity taking into account natural dissipation processes in interlayers based on the rheological method are built. These are the viscoelastic Maxwell, Kelvin–Voigt and Poynting-Thomson models.
The numerical solution of the problem is based on the two-cyclic space-variable decomposition method in combination with monotone grid-characteristic schemes with balanced time steps in layers and interlayers. The issues of program implementations of the proposed algorithms on multiprocessor computer systems with graphical processing units are discussed. Computations of the large number of layers performed on supercomputers allowed to analyze specific "pendulum" waves related to the structural inhomogeneity. The results of numerical analysis demonstrate peculiar quality of planar wave propagation in materials with layered microstructure.

This work was supported by the Russian Foundation for Basic Research (grant no. 11–01–00053) and the Complex Fundamental Research Program no. 18 “Algorithms and Software for Computational Systems of Superhigh Productivity” of the Presidium of RAS.