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

By Sebastian Bielski


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.Comment: 15 pages, 3 figures, 2 table

Topics: Mathematical Physics, 35Jxx
Year: 2011
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