A new fast bem approach to model site effects in alluvial basins

The solution of the elastodynamic equations using integral formulations requires to solve full and non symmetric systems. The use of an iterative solver like GMRES lowers the complexity of the solution (number of operations) to order N2, where N is the number of degrees of freedom (DOFs). The most expensive computational task is the matrix-vector product. For Helmholtz and Maxwell equations, the fast multipole method (FMM) is known to dramatically reduce that cost. This is achieved by (i) using a multipole expansion of the relevant Green's tensor, which allows to reuse element integrals for all collocation points, and (ii) defining a (recursive, multi-level) partition of the region of space enclosing the domain boundary of interest into cubic cells, allowing to optimally cluster influence computations. Moreover, the matrix of the system is not stored with the FMM. So, the complexity (both in CPU time and memory) is found to be N log2 N per iteration. The fast multipole formulation of the boundary element method for 3D elastodynamics in frequency domain is presented in this article. Numerical efficiency and accuracy are assessed on the basis of numerical results obtained for problems having known solutions. Finally, the present FMM-BEMis demonstrated on seismology-oriented examples, namely the study of the diffraction of a plane wave or a point source by a canyon. The influence of the size of the meshed part of the free surface is studied, and computations are performed for nondimensional frequencies higher than those considered in other studies, with which comparisons are made whenever possible