Thu, 30 Nov 2006
16:15
Fisher Room

TBA

Matthew Wingate
(DAMTP, Cambridge)
Thu, 30 Nov 2006
16:00
L3

The weight part of Serre's conjecture for Hilbert modular forms

Fred Diamond
(King's College, London)
Abstract

I will explain the statement of a generalization of Serre's conjecture on mod p Galois representations to the context of Hilbert modular forms. The emphasis will be on the recipe for the set of possible weights (formulated by Buzzard, Jarvis and myself, and partly proved by Gee) and its behavior in some special cases.

Thu, 30 Nov 2006

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted laplacian

Dr Martin Van Gijzen
(Delft University of Technology)
Abstract

Joint work with Yogi Erlangga and Kees Vuik.

Shifted Laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the Helmholtz equation. In this paper we present a comprehensive spectral analysis of the Helmholtz operator preconditioned with a shifted Laplacian. Our analysis is valid under general conditions. The propagating medium can be heterogeneous, and the analysis also holds for different types of damping, including a radiation condition for the boundary of the computational domain. By combining the results of the spectral analysis of the preconditioned Helmholtz operator with an upper bound on the GMRES-residual norm we are able to provide an optimal value for the shift, and to explain the mesh-depency of the convergence of GMRES preconditioned with a shifted Laplacian. We illustrate our results with a seismic test problem.