  We develop a computational framework that leverages the features of
sophisticated software tools and numerics to tackle some of the pressing issues
in the realm of earth sciences. The algorithms to handle the physics of
multiphase flow, concomitant geomechanics all the way to the surface of the
earth and the complex geometries of field cases with surfaces of discontinuity
are stacked on top of each other in a modular fashion which allows for easy use
to the end user. The current focus of the framework is to provide the user with
tools for assessing seismic risks associated with energy technologies as well
as for use in generating forward simulations in inversion analysis from data
obtained using GPS and InSAR. In this work, we focus on one critical aspect in
the development of the framework: the use of computational geometry in a
two-grid method for unstructured tetrahedral meshes
