The numerical solution of the Helmholtz eigenvalue problem is considered.
The application of the boundary element method reduces it to that of a
non-linear eigenvalue problem.
Through a polynomial approximation with respect to the wavenumber, the
non-linear eigenvalue problem is reduced to a standard
generalised eigenvalue problem. The method
is applied to the test problems of
a three-dimensional sphere with an axisymmetric boundary condition
and a two-dimensional square.
Revised software based on this is now available from the author's ABEMFULL package and BEMHELM package.