[BANANA] LA/Opt seminar Wed April 9 (Jim Lambers)

[Michael A. Saunders]

NOTE: We're in a new room during spring.
The Green building is beside Terman and Durand.
The website has a map.

   Linear Algebra and Optimization Seminar (CME510)
   iCME, Stanford University
   http://icme.stanford.edu/seminars/seminars.php

   4:15pm Wed April 9, 2008
   Room GESB134 (Green Earth Sciences Building)

   Dr James Lambers
   iCME (Institute for Computational and Mathematical Engineering)
   Dept of Energy Resources Engineering
   Stanford University
   lambers at stanford.edu
   http://www.stanford.edu/~lambers/


   Implicitly defined high-order operator splittings for
   time-dependent variable-coefficient PDE using modified moments

This talk presents a reformulation of Krylov Subspace Spectral (KSS)
Methods, which build on the many contributions of Gene Golub, et
al. pertaining to moments and Gaussian quadrature in the spectral
domain in order to produce high-order accurate approximate solutions
to variable-coefficient PDE of both parabolic and hyperbolic type.

This reformulation serves two useful purposes.  First, it reveals that
KSS methods are actually high-order operator splittings that are
defined implicitly, in terms of derivatives of the nodes and weights
of Gaussian quadrature rules with respect to a parameter.  Second, it
improves the numerical stability of these methods by removing
cancellation arising from the approximation of these derivatives by
finite differences, instead computing these derivatives analytically.

The talk concludes with new results concerning the application of KSS
methods to systems of coupled PDE, and the time-dependent Schrodinger
equation.