Mathematics, Dartmouth College.
We present and analyze a new method for numerical computation of the
spectrum and eigenfunctions of a planar star-shaped domain with Dirichlet
boundary condition. The method is 'fast' since it is computes a cluster of
eigenfunctions (numbering of order the square-root of the eigenvalue) in
the time usually taken to compute a single one. In practice, with 400
wavelengths across the domain, and relative error 1e-10, this speed-up is
around 1e3. It is related to the little-understood 'scaling method', but,
in constrast, has a rigorous error analysis and allows higher-order
accuracy. We will include some applications to quantum chaos.
Joint work with Andrew Hassell (ANU).
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