Parallel implementation of a spectral scheme for simulations of 3-D dynamic fracture events

The spectral scheme, whose parallel implementation is described in this paper, is currently one of the most efficient computational approaches available to solve a class of fundamental 3-D dynamic fracture problems. The scheme uses a special form of the boundary integral elastodynamic formulation and allows for the solution of the spontaneous motion (initiation, propagation, and arrest) of arbitrary shape planar cracks embedded in a homogeneous or bimaterial medium and subjected to arbitrary loading conditions. The parallel implementation described hereafter allows for the efficient solution of very large dynamic fracture problems, typically one to two orders of magnitudes larger than those available to date. It is based on a stacking scheme that distributes the spectral modes across the processors to achieve balance in memory and CPU time requirements. Although developed for dynamic fracture simulations, the spectral scheme and its parallel implementation are applicable to other problems in computational physics characterized by a convolution operation involving a decaying kernel.