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Two methods for computing bound states of the Helmholtz equation in a finitedomain are presented. The methods are formulated in terms of theDirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) surface integraloperators. They are adapted from the DtN and NtD methods for bound states ofthe Schrodinger equation in R^3. A variational principle that enables the usageof the operators is constructed. The variational principle allows the use ofdiscontinuous (in values or derivatives) trial functions. A numerical examplepresenting the usefulness of the DtN and NtD methods is given.

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