Parallelising the Transfer-Matrix Method using Graphics Processors

Thomas Edwards
Centre for Scientific Computing, Department of Physics, The University of Warwick
The University of Warwick, 2012


   title={Parallelising the Transfer-Matrix Method using Graphics Processors},

   author={Edwards, T.},



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We study the disorder-induced Anderson localisation of a d-dimensional solid, computing the localisation lengths using the Transfer-Matrix Method (TMM) and aiming to develop an efficient parallel implementation to run on Graphics Processing Units (GPUs). In the TMM, a quasi one-dimensional bar of length L >> M is split into slices of size M^(d-1). The Schrodinger equation is reformulated into a 2M x 2M transfer matrix Tn, which is recursively applied at each slice to propagate the wavevectors through the solid. NVidia’s programming architecture for GPUs, CUDA, is used to develop the GPU implementation of the TMM, the CUDA-TMM. Two schemes are developed, the Multi-Parameter Scheme (MPS) and the Single-Parameter Scheme (SPS). In this thesis, various advantages and limitations of both schemes as well as using CUDA in general are discussed.
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