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An Efficient Algorithm For Simulating Fracture Using Large Fuse Networks | | Phani Kumar V.V. Nukala
; Srdjan Simunovic
; | | Date: |
30 Mar 2005 | | Journal: | J. Phys. A: Math. Gen. 36 (2003) 11403-11412 | | Subject: | Materials Science; Statistical Mechanics | cond-mat.mtrl-sci cond-mat.stat-mech | | Abstract: | The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve {it a new large set of linear equations} every time a new lattice bond is broken. To address this problem, we propose an algorithm that combines the multiple-rank sparse Cholesky downdating algorithm with the rank-p inverse updating algorithm based on the Sherman-Morrison-Woodbury formula for the simulation of progressive fracture in disordered quasi-brittle materials using discrete lattice networks. Using the present algorithm, the computational complexity of solving the new set of linear equations after breaking a bond reduces to the same order as that of a simple {it backsolve} (forward elimination and backward substitution) {it using the already LU factored matrix}. That is, the computational cost is $O(nnz({f L}))$, where $nnz({f L})$ denotes the number of non-zeros of the Cholesky factorization ${f L}$ of the stiffness matrix ${f A}$. This algorithm using the direct sparse solver is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) iterative solvers, and eliminates the {it critical slowing down} associated with the iterative solvers that is especially severe close to the critical points. Numerical results using random resistor networks substantiate the efficiency of the present algorithm. | | Source: | arXiv, cond-mat/0503719 | | Services: | Forum | Review | PDF | Favorites | |
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