Abstract
We discuss a new method of analyzing two-dimensional eigenvalue problems described by Helmholtz's equation. A general solution is assumed as a linear combination of plane waves which have the same wave number and travel in different directions. Nodal points are located only on the boundary of a convex domain which has an arbitary shape. A set of equations similar to finite-element equations can be derived from the general solutions. Eigenvalues obtained by this method are very close to the exact values. This method is effective in simplifying of the programming and in shortening computational time.
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