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In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical method for the voice generation problem. The basic mathematical model for the voice generation is the Helmholtz equation in an unbounded region. Introducing an artificial boundary, we divide the unbounded region into a bounded region and the rest unbounded one with a simple shape. We apply the finite element method for the equation in the bounded region imposing an artificial boundary condition given through the Dirichlet to Neumann (DtN) mapping on the artificial boundary. We then compute the frequency response function or the formant curve by which we can simulate the voice generation process for various vowels. The complex eigenvalues related to the Helmholtz equation control the peaks of the frequency response function known as formants. We give the variational formulas for the complex eigenvalues with respect to the variation of vocal tract boundary. [ABSTRACT FROM AUTHOR]