Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step

The purpose of this article is to develop a grid-characteristic method for high-performance computing systems using unstructured tetrahedral hierarchical meshes, a multiple time step and the high-order interpolation for simulating complex spatial dynamic processes in heterogeneous environments. This method has the precise formulation of contact conditions and is suitable for the physically correct solution of the seismology and seismic prospecting problems in complex heterogeneous environments. The use of the hierarchical meshes allows to take into account a large number of non-homogeneous inclusions (cracks, cavities, etc.). The use of this grid-characteristic method makes it possible to use the multiple time step and thereby increase productivity and significantly reduce the computation time. The methods developed for high-order interpolation on unstructured tetrahedral meshes can solve the problems of seismology and seismic prospecting with the approximation in space to the fifth degree inclusive.