A third-order boundary element method for scattering of elastic shells

In the present work we present a third-order boundary element method for the prediction of sound scattered by rigid or elastic shells impinged by planar pressure waves. The so-called Fictitious Eigenvalues Difficulty introduced by the boundary element method approach (that consists of the existence of spurious resonances for the frequencies of related interior problem) is overcome by the CONDOR technique by Burton and Miller which corresponds to the use of a suitable linear combination of the KirchhofFHelmoltz equation with that obtained by taking its normal derivative. The resulting boundary integral equation is here solved by a piecewise bicubic discretization. Numerical results obtained for radiation and scattering problems are presented, and validated through comparison with analytical solutions. Numerical analysis shows that the convergence rate is of order h3 (h being the typical size of the elements), indicating that this is a true third-order method.