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NJIT Applied Mathematics Colloquium

Friday, April 23, 2010, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology

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Optimal finite-difference grids for Neumann-to-Dirichlet operators

Vladimir Druskin

Schlumberger Doll Research

For many applications 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 model reduction in the spectral domain, and gives exponential super-convergence of the Neumann-to-Dirichlet (NtoD ) map. The technique uses simple second order finite-difference approximations with optimized placement of the grid points. The fact that the NtoD map is well approximated makes the technique ideal for inverse problems, domain decomposition and absorbing boundary conditions.