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S (2004) DirichlettoNeumann and NeumanntoDirichlet embedding methods for bound states of the Schrödinger equation. Phys Rev A 70:042103
"... Two methods for computing bound states of the Helmholtz equation in a finite domain are presented. The methods are formulated in terms of the DirichlettoNeumann (DtN) and NeumanntoDirichlet (NtD) surface integral operators. They are adapted from the DtN and NtD methods for bound states of the Sc ..."
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Two methods for computing bound states of the Helmholtz equation in a finite domain are presented. The methods are formulated in terms of the DirichlettoNeumann (DtN) and NeumanntoDirichlet (NtD) surface integral operators. They are adapted from the DtN and NtD methods for bound states of the Schrödinger 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. 1