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Compressed Symmetric Graphs for the Simulation of Super Carbon Nanotubes

Burger, Michael and Bischof, Christian and Wackerfuß, Jens (2016):
Compressed Symmetric Graphs for the Simulation of Super Carbon Nanotubes.
In: Proceedings of the 2016 International Conference on High Performance Computing & Simulation, Innsbruch, Austria, Innsbruch, Austria, 2016, [Online-Edition: http://hpcs2016.cisedu.info/],
[Conference or Workshop Item]

Abstract

In this paper, we present an extremely space-saving, yet parallelizable, data structure called Compressed Symmetric Graphs (CSGs) for the simulation of Super Carbon Nanotubes (SCNTs) modeled by a graph algebra. CSGs can drastically reduce the amount of data to represent a SCNT by exploiting inherent symmetry and hierarchy to dynamically reconstruct symmetric parts from base elements as needed. This new graph structure is integrated in an existing matrix-free solving approach for simulating the mechanical behavior of SCNTs. We extend previous investigations on structural symmetry in SCNTs to now simultaneously exploit translational and rotational symmetry, thus multiplying their effects. As a result, we can reach compression ratios of over 100 for some SCNT configurations. The memory demand is further reduced by replacing the m-tuples identifying the nodes in the graph model via a structure-related compression by a serial index that can be unfolded on demand. Finally, we use still available RAM as a software-controlled cache for storing intermediate values, reducing recomputations. In this fashion, our code can represent very large configurations, but makes optimal use of the hardware at hand. We investigate for order 0 and 1 SCNTs the impact of the data access-time in CSGs on the total runtime and a suitable OpenMP parallelization strategy for minimizing this influence. We demonstrate that as a result, the new CSGs approach significantly reduces the runtime, by a factor between 1:3 and 12. While the graph algebra underlying this work was designed for the representation of SCNTs, we believe that the algorithmic principles with respect to the exploitation of structure and efficient software design are relevant to other graph settings, where hierarchy and replication play an important role in the graph design. In these cases, CSGs can help to overcome the per node/core memory-capacity limitation of current HPC systems.

Item Type: Conference or Workshop Item
Erschienen: 2016
Creators: Burger, Michael and Bischof, Christian and Wackerfuß, Jens
Title: Compressed Symmetric Graphs for the Simulation of Super Carbon Nanotubes
Language: English
Abstract:

In this paper, we present an extremely space-saving, yet parallelizable, data structure called Compressed Symmetric Graphs (CSGs) for the simulation of Super Carbon Nanotubes (SCNTs) modeled by a graph algebra. CSGs can drastically reduce the amount of data to represent a SCNT by exploiting inherent symmetry and hierarchy to dynamically reconstruct symmetric parts from base elements as needed. This new graph structure is integrated in an existing matrix-free solving approach for simulating the mechanical behavior of SCNTs. We extend previous investigations on structural symmetry in SCNTs to now simultaneously exploit translational and rotational symmetry, thus multiplying their effects. As a result, we can reach compression ratios of over 100 for some SCNT configurations. The memory demand is further reduced by replacing the m-tuples identifying the nodes in the graph model via a structure-related compression by a serial index that can be unfolded on demand. Finally, we use still available RAM as a software-controlled cache for storing intermediate values, reducing recomputations. In this fashion, our code can represent very large configurations, but makes optimal use of the hardware at hand. We investigate for order 0 and 1 SCNTs the impact of the data access-time in CSGs on the total runtime and a suitable OpenMP parallelization strategy for minimizing this influence. We demonstrate that as a result, the new CSGs approach significantly reduces the runtime, by a factor between 1:3 and 12. While the graph algebra underlying this work was designed for the representation of SCNTs, we believe that the algorithmic principles with respect to the exploitation of structure and efficient software design are relevant to other graph settings, where hierarchy and replication play an important role in the graph design. In these cases, CSGs can help to overcome the per node/core memory-capacity limitation of current HPC systems.

Title of Book: Proceedings of the 2016 International Conference on High Performance Computing & Simulation
Volume: 2016
Place of Publication: Innsbruch, Austria
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Scientific Computing
Zentrale Einrichtungen > University IT-Service and Computing Centre (HRZ) > Hochleistungsrechner
Exzellenzinitiative
Zentrale Einrichtungen > University IT-Service and Computing Centre (HRZ)
Zentrale Einrichtungen
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Exzellenzinitiative > Graduate Schools
Event Location: Innsbruch, Austria
Date Deposited: 13 Jun 2016 11:30
Official URL: http://hpcs2016.cisedu.info/
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