## Colloquium-Vladimir Druskin (Schlumberger Doll Research)-Finite-difference Gaussian rules for Dirichlet-to-Neumann operators, perfectly matched layers, and inverse problems

Mathematics - Colloquium

Friday, February 28, 2014

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: 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 techniques. It yields spectral superconvergence at a priori chosen boundaries using simple standard staggered second-order finite-differrence or finite-volume schemes. In particular, this approach has shown good success in applications to optimal discretization of perfectly matched layers and the finite-difference solution of the inverse electrical-impedance tomography and wave problems. Contributors: Liliana Borcea, David Ingerman, Leonid Knizhnerman, Alexander Mamonov, Shari Moskow, Fernando Guevara Vasques, Mikhail Zaslavsky

Suggested Audiences:
Adult, College

E-mail:
ma-chair@wpi.edu

Last Modified: February 12, 2014 at 10:15 AM

## Colloquium-Vladimir Druskin (Schlumberger Doll Research)-Finite-difference Gaussian rules for Dirichlet-to-Neumann operators, perfectly matched layers, and inverse problems

Mathematics - Colloquium

Friday, February 28, 2014

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: 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 techniques. It yields spectral superconvergence at a priori chosen boundaries using simple standard staggered second-order finite-differrence or finite-volume schemes. In particular, this approach has shown good success in applications to optimal discretization of perfectly matched layers and the finite-difference solution of the inverse electrical-impedance tomography and wave problems. Contributors: Liliana Borcea, David Ingerman, Leonid Knizhnerman, Alexander Mamonov, Shari Moskow, Fernando Guevara Vasques, Mikhail Zaslavsky

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: February 12, 2014 at 10:15 AM