An efficient GPU algorithm for tetrahedron-based Brillouin-zone integration

Daniel Guterding, Harald O. Jeschke
Lucht Probst Associates, Grosse Gallusstrasse 9, 60311 Frankfurt am Main, Germany, European Union
arXiv:1710.10789 [physics.comp-ph], (30 Oct 2017)


   title={An efficient GPU algorithm for tetrahedron-based Brillouin-zone integration},

   author={Guterding, Daniel and Jeschke, Harald O.},






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We report an efficient algorithm for calculating momentum-space integrals in solid state systems on modern graphics processing units (GPUs). We extend the tetrahedron method by Bl"ochl et al.~to the more general case of the integration of a momentum as well as energy dependent quantity and implement the algorithm based on the CUDA programming framework. We test this method by applying it to a simple example, the calculation of the orbital-resolved density of states. We benchmark our code on the problem of calculating the orbital-resolved density of states in an iron-based superconductor and discuss the design choices made in the implementation. Our algorithm delivers large speedups of up to a factor $sim165$ also for moderately sized workloads compared to standard algorithms executed on central processing units (CPUs).

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