A fast directional boundary element method for wideband multi-domain elastodynamic analysis

Abstract A fast directional boundary element method for wideband multi-domain elastodynamic analysis is developed. The directional low rank property of the elastodynamic kernel is proved, which serves as the theoretical basis of the fast directional algorithm. The boundary integral evaluation is accelerated domain by domain. For each domain, the octree is divided into low frequency and high frequency regimes according to its S-wave number. The computation in the low frequency regime is the same with the kernel independent fast multipole method, while the high frequency regime is computed efficiently by applying the parabolic low rank property of the kernels on directional wedges. The matrices on only one directional wedge for each level have to be calculated, since that for other directions can be obtained by coordinate frame rotations. Thus the harmonic responses for any frequencies can be computed efficiently. Numerical results show that the computational complexity for wideband multi-domain elastodynamic problems is successfully brought down to O(NlogαN). Its applications to viscoelastic materials and inverse problems are also validated.