Exploiting structural properties during carbon nanotube simulation

Abstract

In this paper, we present a novel matrix-free algorithm for the simulation of the mechanical behavior of carbon nanotubes (CNTs). For small deformations, this algorithm is capable of exploiting the inherent symmetry within CNT structures. The symmetry information is encoded with a graph algebra (GA) construction process and preserved within a tuple based atom-indexing. The exploitation of symmetry leads to a reduction of the needed calculations by a factor of more than 100 in the case of larger CNTs. Combining the usage of symmetry information with a new potential caching mechanism, our software is able to store even large tubes in a compressed way with only a few megabytes of data. Altogether, our implementation allows a matrix-free, resourceaware simulation of CNTs. For larger cases it is only about the factor 1.45 -1.6 slower than the reference solution with a fully assembled stiffness matrix, but consumes twelve times less memory. Also first results of the parallelization of our new algorithm are presented.