Imaging and Computing Seminar

Vladimir Druskin

Title:
Optimal finite-difference grids for Neumann-to-Dirichlet operators.

Abstract:
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 supecrconvergence of the Neumann-to-Dirichlet 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 condition.

Contributors: Sergey Asvadurov, Liliana Borcea, Murthy Guddatti, Fernando Guevara Vasquez, David Ingerman, Leonid Knizhnerman, Alexander Mamonov and Shari Moskow