Large scale simulation of fracture networks

Computational modeling of fracture in disordered (heterogeneous) media using discrete lattice models is often limited to small system sizes due to high computational cost involved in re-solving the governing system of equations every time a new lattice bond is broken. For two-dimensional simulations, this paper proposes an efficient algorithm based on multiple-rank sparse Cholesky downdating scheme. Based on the proposed algorithm, the authors present simulation results for large 2D lattice systems (e.g., L=1024), which to the authors knowledge, is so far the largest lattice system used in studying the damage evolution. For three-dimensional simulations, we propose efficient algorithms based on iterative schemes. The block-circulant preconditioner and the current algorithm based on superfast Toeplitz solver are intended for large-scale 3D discrete lattice simulations.