Abstract
Eigenvalues are obtained by means of a Helmholtz integral equation formulation for wave resonances in two- and three-dimensional enclosed regions. Examples of circular and spherical regions are given to compare this approach to the simpler but less general separation of variables method. An example of a triangularly shaped two-dimensional region is given to illustrate the advantages of this approach, i.e., that only surface values of the dependent variables appear, allowing a fine grid to be used with relatively few points, as compared to a standard finite difference approach for a nonseparable geometry.
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