Spectrally-Matched Grids for Dirichlet-to-Neumann Operators
The spectrally matched finite-difference grids (a.k.a. FD Gaussian rules or optimal grids) were originally invented to obtain high accuracy of Dirichlet-to-Newman maps for truncation of unbounded computational domains. .Such grids yield spectral superconvergence at a priori chosen boundaries or points (receivers) using simple standard staggered second order FD or FV schemes. A similar approach was also developed for Bubnov-Galerkin FEM. with linear elements. I will review applications of the spectrally matched grids for the solution of some direct and inverse PDE problems arising in remote sensing. Contributors: Liliana Borcea, Murthy Guddati, David Ingerman, Leonid Knizhnerman, Shari Moskow, Fernando Guevara Vasques.
Vladimir Druskin, Schlumberger Doll Research