Computational Mathematics and Scientific Computing Seminar

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Finite-difference Gaussian Rules for Dirichlet-to-Neumann Operators, Perfectly Matched Layers and Inverse Problems

Speaker: Vladimir Druskin, Schlumberger Doll Research

Location: Warren Weaver Hall 1302

Date: April 18, 2014, 10 a.m.

Synopsis:

The finite-difference Gaussian rules (a.k.a. spectrally-matched or optimal grids) were originally invented to obtain high accuracy of Dirichlet-to-Newman maps for truncation of unbounded computational domains. Their construction is mainly based on Stieltjes-Krein continued fraction technique. It yields spectral superconvergence at a priori chosen boundaries using simple standard staggered second order FV schemes. In particular, this approach showed good success in application to optimal discretization of perfectly matched layers and the finite-difference solution of the inverse EIT and wave problems. Contributors: Liliana Borcea, Stefan Guettel, David Ingerman, Leonid Knizhnerman, Alexander Mamonov, Shari Moskow, Fernando Guevara Vasques, Mikhail Zaslavsky