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

Phani Kumar V.V. Nukala; Srdan Šimunović

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

Phani Kumar V.V. Nukala, Srdan Šimunović

Multiscale Materials

Research output: Contribution to journal › Conference article › peer-review

Abstract

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.

Original language	English
Article number	037
Journal	Proceedings of Science
Volume	23
State	Published - 2005
Event	2005 International Conference on Statistical Mechanics of Plasticity and Related Instabilities, SMPRI 2005 - Bangalore, India Duration: Aug 29 2005 → Sep 2 2005

Funding

In this paper, we present three alternate approaches to increase the efficiency of algorithms used in large scale 3D simulation of fracture using discrete lattice networks such as fuse, spring and beam networks. These approaches, namely, efficient preconditioners, krylov subspace recycling, and massive parallelization of the algorithms significantly reduce the computational time required for simulating large 3D lattice systems. Our preliminary studies on a 3D cubic lattice system of size L = 64 indicate that krylov subspace recycling can reduce the computational time by as much as 30%, and a straight forward massive parallelization of our iterative schemes using block-circulant preconditioners can reduce the computational time from 14 days to a day. However, even with these novel approaches, analysis of a 3D lattice system of size L = 200 appears to be impractical, if not impossible. Currently, we are exploring the alternatives of combining massive parallelization with krylov subspace recycling techniques and efficient preconditioners, the combination of which promises to significantly reduce the computational cost associated with simulating large 3D lattice systems of the order of L = 200. Acknowledgment PKVVN is sponsored by the Mathematical, Information and Computational Sciences Division, Office of Advanced Scientific Computing Research, U.S. Department of Energy under contract number DE-AC05-00OR22725 with UT-Battelle, LLC.

Funders	Funder number
U.S. Department of Energy	DE-AC05-00OR22725
Advanced Scientific Computing Research

Cite this

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title = "Computational challenges in the large-scale simulations of fracture in disordered media",

abstract = "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.",

author = "Nukala, {Phani Kumar V.V.} and Srdan {\v S}imunovi{\'c}",

note = "Publisher Copyright: {\textcopyright} Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.; 2005 International Conference on Statistical Mechanics of Plasticity and Related Instabilities, SMPRI 2005 ; Conference date: 29-08-2005 Through 02-09-2005",

year = "2005",

language = "English",

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journal = "Proceedings of Science",

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T1 - Computational challenges in the large-scale simulations of fracture in disordered media

AU - Nukala, Phani Kumar V.V.

AU - Šimunović, Srdan

N1 - Publisher Copyright: © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

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SN - 1824-8039

VL - 23

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T2 - 2005 International Conference on Statistical Mechanics of Plasticity and Related Instabilities, SMPRI 2005

Y2 - 29 August 2005 through 2 September 2005

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

Abstract

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