TY - JOUR

T1 - An efficient algorithm for simulating fracture using large fuse networks

AU - Nukala, Phani Kumar V.V.

AU - Simunovic, Srdan

PY - 2003/11/14

Y1 - 2003/11/14

N2 - The high computational cost involved in modelling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve 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 backsolve (forward elimination and backward substitution) using the already LU factored matrix. That is, the computational cost is O (nnz(L)), where nnz(L) denotes the number of non-zeros of the Cholesky factorization L of the stiffness matrix A. This algorithm using the direct sparse solver is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) iterative solvers, and eliminates the 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.

AB - The high computational cost involved in modelling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve 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 backsolve (forward elimination and backward substitution) using the already LU factored matrix. That is, the computational cost is O (nnz(L)), where nnz(L) denotes the number of non-zeros of the Cholesky factorization L of the stiffness matrix A. This algorithm using the direct sparse solver is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) iterative solvers, and eliminates the 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.

UR - http://www.scopus.com/inward/record.url?scp=0242508326&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/45/004

DO - 10.1088/0305-4470/36/45/004

M3 - Article

AN - SCOPUS:0242508326

SN - 0305-4470

VL - 36

SP - 11403

EP - 11412

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 45

ER -