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

Abstract

The purpose of the present paper is to develop a grid-characteristic method for high-performance computer 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 seismology and seismic prospecting problems in complex heterogeneous environments. The use of the hierarchical meshes allows us to take into account a large number of nonhomogeneous inclusions (cracks, cavities, etc.). The use of this grid-characteristic method makes it possible to use a 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 approximation in space of up to the fifth degree (inclusive).