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2006.367: Computed eigenmodes of planar regions

2006.367: Lloyd N. Trefethen and Timo Betcke (2005) Computed eigenmodes of planar regions. AMS Contemporary Mathematics.

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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 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MIMS number:2006.367
Deposited By:Dr. Timo Betcke
Deposited On:14 September 2006

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