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Computational Techniques for Efficient Carbon Nanotube Simulation
Ashok Srinivasan Computer Science Florida State University Namas Chandra Mechanical Engineering Florida State University
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Outline Background Parallel nanotube simulation Nanocomposites
Parallelization Conclusions and future work
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Background Uses of Carbon nanotubes CNT properties Materials NEMS
Transistors Displays Etc CNT properties Can span 23,000 miles without failing due to its own weight 100 times stronger than steel Many times stiffer than any known material Conducts heat better than diamond Can be a conductor or insulator without any doping Lighter than feather
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Sequential computation
Molecular dynamics, using Brenner’s potential Short-range interactions Neighbors can change dynamically during the course of the simulation Computational scheme Find force on each particle due to interactions with “close” neighbors Update position and velocity of each atom
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Force computations Pair interactions Bond angles Four body
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Profile of execution time
1: Force 2: Neighbor list 3: Predictor/corrector 4: Thermostating 5: Miscellaneous
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Profile for force computations
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Parallel nanotube simulation
Shared memory Message passing Load balancing
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Shared memory parallelization
Do each of the following loops in parallel For each atom Update forces due to atom i If neighboring atoms are owned by other threads, update an auxiliary array For each thread Collect force terms for atoms it owns Srivastava, et al, SC-97 and CSE 2001 Simulated 105 to 107 atoms Speedup around 16 on 32 processors Include long-range forces too Lexical decomposition
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Message passing parallelization
Decompose domain into cells Each cell contains its atoms Assign a set of adjacent cells to each processor Each processor computes values for its cells, communicating with neighbors when their data is needed Caglar and Griebel, World scientific, 1999 Simulated 108 atoms on up to 512 processors Linear speedup for 160,000 atoms on 64 processors
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Load balancing
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Nanocomposites Matrix-nanotube interface modeled with springs
An extra force term computed for atoms attached to springs Springs can break, requiring substantial increase in computations in that region Spring Polymer matrix
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Parallelization Distributed shared memory
Balance the load Ensure locality of data Simple lexical approach will result in load imbalance Balanced lexical Adjust the domain size
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Breadth first search We want to ensure locality too
Balanced Breadth First Search Perform a breadth first search on the atom interaction graph
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Use general purpose software
Other approaches Use general purpose software Jostle Metis ParMetis
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Experimental parameters
Nanotube with 1000 atoms Spring probability: 0.05 Probability of a spring breaking in an iteration: 0.01 Load increase factor due to spring break: 200 Disturbance region depth: 3 Number of time steps: 100
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Load imbalance
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Non-local interactions
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Load balancing time
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Variation of load with time
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Conclusions and future work
Neighbor search Parallelization Current approaches appear inadequate General purpose software is too slow Special purpose techniques appear promising Stochastic versions of certain current techniques possible Multi-scale simulation of nano-composites MD at nano-scale and FEM at larger scale
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