Computed eigenmodes of planar regions

Trefethen, Lloyd N. and Betcke, Timo (2005) Computed eigenmodes of planar regions. AMS Contemporary Mathematics. (In Press)

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Abstract

Recently developed numerical methods make possible the high-accuracy computation of eigenmodes of the Laplacian for a variety of "drums" in two dimensions. A number of computed examples are presented together with a discussion of their implications concerning bound and continuum states, isospectrality, symmetry and degeneracy, eigenvalue avoidance, resonance, localization, eigenvalue optimization, perturbation of eigenvalues and eigenvectors, and other matters.

Item Type: Article
Uncontrolled Keywords: billiards, drums, Helmholtz equation, level repulsion, membranes, quantum chaos, Schrödinger operator
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr. Timo Betcke
Date Deposited: 14 Sep 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/594

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