Separation of variables in perturbed cylinders

Details Separation of variables in perturbed cylinders Separation of variables in perturbed cylinders

2000-12-14

arxiv.org/abs/math/0012113v1

Mathematics

Spectral Theory

LaTeX 2e, 18 pages, 6 figures

Scientific paper

10.1006/jcph.2001.6913

We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the Fourier decomposition method. The ODE system obtained in this way is then solved numerically yielding the eigenvalues of the operator. The same approach allows us to find complex resonances arising in some non-compact domains. We discuss numerical examples related to quantum waveguide problems.

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