Computational challenges in the large-scale simulation of fracture in disordered media

Details Computational challenges in the large-scale simulation of fracture in disordered media Computational challenges in the large-scale simulation of fracture in disordered media

Nov 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006smpr.confe..37n&link_type=abstract

Proceedings of the International conference on Statistical Mechanics of Plasticity and Related Instabilities. August 29-Septembe

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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 gov- erning 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 simula- tions, 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 ef- ficient 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 sub- space 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.

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