Title: Optimal finite-difference grids for  Neumann-to-Dirichlet problems


			     Vladimir Druskin,
                          Scientific Advisor, Ph.D.
                         Schlumberger Doll Research
			     36 Old Quarry Road
			  Ridgefield, CT 06877, US
               e-mail: vdruskin@ridgefield.oilfield.slb.com


Abstract:
For many applications, such as geophysics, the solution of a partial 
differential equation is produced by local sources and is needed only at 
receiver locations, and not in the entire domain. In this talk, we introduce 
and discuss new developments with a rigorous approach to targeted grid 
refinement which is based on rational approximation of the Neumann-to-Dirichlet
(ND) map in the spectral domain. The technique uses simple finite difference 
approximations with optimized placement of the grid points. The fact that the 
ND map is well approximated makes the technique ideal for inverse problems, 
domain decomposition and absorbing boundary conditions.