A New Technique Combining Eigenfunction Expansions and Boundary Elements to Solve Acoustic Radiation Problems

A central problem in noise control involves the calculation of sound radiation and the holographic reconstruction of sources. A standard method for such calculations employs boundary elements and the surface Helmholtz integral equation (SHIE). However, difficulties occur at frequencies for which a congruent pressure-release boundary would have interior resonances. In such cases the SHIE does not have a unique solution and the matrix used in the boundary element method is singular. This talk will present a new technique which employs both eigenfunction expansions (typically using spherical wavefunctions) and boundary element matrices. This new method avoids problems with internal resonances and singular matrices, does not require adding internal “CHIEF” points, and permits fast and accurate holographic reconstructions for arbitrarily shaped sources. Advantageous operations termed “iterative deepening”, which automatically discards unnecessary eigenfunctions and detects any symmetries in the problem, and “forward refinement” with “parametric relaxation”, which guarantees convergence to a correct and accurate solution, will be presented. Application of this new method to inverse propagation will be discussed.