HELMHOLTZ EIGENVALUE ANALYSIS BY BOUNDARY ELEMENT METHOD

A new and robust scheme for the eigenvalue analysis of the Helmholtz differential equation by the boundary element method (BEM) is developed in this paper. Unlike the existing methods in which a highly complicated transcendental equation including the unknown wavenumbers appears, the present method can reduce the computational task greatly with the help of the Multiple Reciprocity Boundary Element formulation in terms of the fundamental solution for the Laplace equation and related simple calculations for polynomials. The Newton method is employed for determination of the desired eigenvalues. Two-dimensional problems with various homogenous boundary conditions are solved to show the versatility of the proposed scheme. © 1993 Academic Press limited.