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We have successfully applied an FM-BIEM with diagonal forms to the analysis of three dimensional scattering of elastic waves by cracks. We have found that a 4 moment diagonal form FM-BIEM formulation for elastodynamics in 3D is possible, and is faster than the corresponding FM-BIEM formulation with the Wigner-3j symbols in problems with moderate wave numbers.

As we have mentioned above, diagonal forms are known to have numerical instabilities in low frequency problems. It would be necessary to carry out more numerical experiments to investigate such numerical instabilities quantitatively for further applications of the proposed techniques in practical problems.