Evaluation of the hypersingular boundary integral equation for acoustic wave-propagation simulations

We have developed a hypersingular boundary integral equation (BIE) approach to simulate wave scattering by inclusions such as karstic cavities and gypsum salts. The solution of conventional BIEs for exterior boundary value problems is of nonuniqueness and numerical instability at characteristic wavenumbers (corresponding to fictitious resonant frequencies). With the hypersingular boundary integral operator, we can handle this problem, but with the difficult-to-calculate hypersingular kernels. Our method to evaluate the singular part in the operator is more efficient than other singularity-elimination techniques. Numerical examples validate the method by comparing with the analytical solution.