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DY: Fachverband Dynamik und Statistische Physik
DY 40: Posters II
DY 40.34: Poster
Donnerstag, 17. März 2011, 17:00–19:00, P3
Parallelising the transfer-matrix method in disordered systems using graphics processors — •Thomas Edwards and Rudolf Römer — University of Warwick, Coventry, United Kingdom
We study the disorder-induced Anderson localisation of a d-dimensional solid and compute the localisation lengths using the transfer matrix method (TMM), seeking a parallel implementation to run on graphics processing units (GPU’s). In the TMM, a quasi one-dimensional bar of length L ≫ M is split into slices of size Md−1. The Schrödinger equation is recursively applied such that the wave function at the future slice ψi+1 is computed from the past and present slices, ψi and ψi−1. Reformulating the Schrödinger equation into a transfer matrix and repeating multiplications of these matrices at each slice gives the ’global transfer matrix’, which maps the wave functions from one side of the bar to the other. The minimum eigenvalue computed from this matrix gives the localisation length. To obtain the minimum eigenvalue and prevent numerical instabilities resulting from the exponential increase in the eigenvalues, the eigenvectors must be re-orthonormalised after every few matrix multiplications. This takes a considerable amount of time, as does computing the transfer matrices themselves, making it crucial to efficiently parallelise the TMM code. To do this we use CUDA, NVIDIA’s proprietary GPU programming language. The speed-up gained from running the code on NVIDIA GPU’s is then analysed using the Karp-Flapp metric.