Abstract
The paper presents the state-of-the-art algorithmic developments for
simulating the fracture of disordered quasi-brittle materials using
discrete lattice systems. Large scale simulations are often required
to obtain accurate scaling laws; however, due to computational
complexity, the simulations using the traditional algorithms were limited to
small system sizes. In our earlier work, we have developed two algorithms: a
multiple sparse Cholesky downdating scheme for simulating 2D random
fuse model systems, and a block-circulant preconditioner for simulating
3D random fuse model systems. Using these algorithms, we were able to
simulate fracture of {\it largest ever} lattice system sizes ($L = 1024$ in 2D,
and $L = 64$ in 3D) with extensive statistical sampling. Our recent
massively parallel simulations on $1024$ processors of Cray-XT3 and
IBM Blue-Gene/L have further
enabled us to explore fracture of 3D lattice systems of size $L = 128$,
which is a significant computational achievement.
Based on these large-scale simulations, we analyze
the scaling of crack surface roughness.
