Spectrally matched finite-difference grids (aka FD Gaussian rules or optimal grids) were originally invented to obtain high accuracy at targeted areas of computational domain [7]. They produce exponential superconvergence at a priori chosen points (receivers) or boundaries using simple standard staggered second order FD or FV schemes The optimal grids were implemented for the solution of forward and inverse PDE problems for Maxwell and elasticity equations arising in oil exploration. This is joint work with Liliana Borcea,Fernando Guevara Vasques, David Ingerman, Leonid Knizhnerman, Shari Moskow and others.