Regensburg 2007 – wissenschaftliches Programm

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HL: Fachverband Halbleiterphysik

HL 13: Poster 1

HL 13.2: Poster

Montag, 26. März 2007, 15:00–17:30, Poster A

The application of multigrid methods to the Helmholtz/Anderson problem — •Rudolf Roemer and Sarah Mallion — Centre for Scientific Computing, University of Warwick, Coventry, UK

The similarities of the Helmholtz equation to the Schrödinger equation make it an ideal testing ground for programs designed to solve the latter. Multigrid methods are one way of solving the superficially similar Laplace equation and they can be highly efficient and easily adaptable to the specifics of an individual problem. The very nature of the multigrid process however, with its repeated interpolation and smoothing steps prevents it from converging to rapidly oscillating solutions such as those occurring with the Helmholtz equation. This is particularly problematic when the diagonal term includes randomness - the Anderson model. We propose the use of the comparatively slower varying WKB ansatz as an assumed form for the solution to the Helmholtz equation. This, with appropriately set of re-derived discrete differential operators, has the potential to negate the inherent problems of the Laplacian multigrid solver and allows convergence even to the highly oscillating solutions of the Helmholtz equation.