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arXiv · 1102.5259

Dirichlet-to-Neumann and Neumann-to-Dirichlet methods for bound states of the Helmholtz equation

Sebastian Bielski
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Abstract

Two methods for computing bound states of the Helmholtz equation in a finite domain are presented. The methods are formulated in terms of the Dirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) surface integral operators. They are adapted from the DtN and NtD methods for bound states of the Schrodinger equation in R^3. A variational principle that enables the usage of the operators is constructed. The variational principle allows the use of discontinuous (in values or derivatives) trial functions. A numerical example presenting the usefulness of the DtN and NtD methods is given.

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Sebastian Bielski. 2011-02-25. Dirichlet-to-Neumann and Neumann-to-Dirichlet methods for bound states of the Helmholtz equation. https://arxiv.org/abs/1102.5259

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