Approximation of the acoustic and elastic wave equations by generalized finite difference stencils applied the unstructured grids.

Resumo

Classical finite difference methodologies, obtained through Taylor series expansions of the functions,
are feasible only when the points are distributed on structured or Cartesian grids defined over rectangular domains

or mapped to rectangles. In this paper we present a technique capable of generating approximations for the two-
dimensional acoustic and elastic wave equations on structured and unstructured meshes over more general domains.

The stencils were calculated at each point of the arbitrary grid by interpolation techniques and the results shown
that the order of accuracy, obtained when the structured grid is used, is maintain to case unstructured and minimum
number of points of the stencils.