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02/27/04 Colloquium
DR. VLADIMIR DRUSKIN
SCHLUMBERGER DOLL RESEARCH
RIDGEFIELD, CT
SCHLUMBERGER DOLL RESEARCH
RIDGEFIELD, CT
Optimal Finite-Difference Grid for Neumann-to-Dirichlet Operators
Abstract: For many applications, such as remote sensing, 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. We introduce and discuss new developments with a rigorous approach to targeted grid refinement, which is based on rational approximation and continued fraction representation 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.