Non-singular boundary element method on impedances of three-dimensional rectangular foundations

A non-singular boundary element method, as well as Green's functions of distributed loads, is developed to calculate the impedances of three-dimensional rectangular foundations. Both the sources and the targets for boundary element method are on the true foundation interface, instead of an additional auxiliary interface for sources or for targets, and the gradient variation of Green's functions near the sources is smooth, which ensures the stability, precision and efficiency of the method. Foundation impedances in multi-layered half-space are concerned to consider the stratifications of the building sites. Compared to axisymmetric foundations, large calculation task and storage requirement are expected, so MPI parallelism for clustered computers is described and various techniques are used to reduce the computer task effectively. The method is immediately used for impedances of arbitrary-shaped foundations and other scattering problems associated with unbounded half-space.