出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：Computational modeling of fracture in disordered materials using discrete lattice models is often
limited to small system sizes due to high computational cost associated with re-solving the governing
system of equations every time a new lattice bond is broken. Previously, we proposed an
efficient algorithm based on multiple-rank sparse Cholesky downdating scheme for 2D simulations,
and an iterative scheme using block-circulant preconditioners for 3D simulations. Based on
these algorithms, we were able to simulate large 2D lattice systems (e.g., L = 1024). However,
despite these algorithmic advances, the largest 3D lattice system that we were able to solve was
limited to a size of L = 64. In this paper, we present three alternate approaches, namely, the efficient
preconditioners, krylov subspace recycling, and massive parallelization of the algorithms,
the combination of which promise to significantly reduce the computational cost associated with
simulating large 3D lattice systems of sizes L = 200. The main idea associated with krylov subspace
recycling is to retain a subspace determined while solving the current system and reuse it to
reduce the cost of solving the subsequent system obtained after removing the new broken bond.
Preliminary numerical simulation of fracture using 3D random fuse networks of sizes L = 64
substantiates the efficiency of the present algorithms.
