We report an efficient algorithm for calculating momentum-space integrals in solid state systems on modern graphics processing units (GPUs). Our algorithm is based on the tetrahedron method, which we demonstrate to be ideally suited for execution in a GPU framework. In order to achieve maximum performance, all floating point operations are executed in single precision. For benchmarking our implementation within the CUDA programming framework we calculate the orbital-resolved density of states in an iron-based superconductor. However, our algorithm is general enough for the achieved improvements to carry over to the calculation of other momentum integrals such as, e.g. susceptibilities. If our program code is integrated into an existing program for the central processing unit (CPU), i.e. when data transfer overheads exist, speedups of up to a factor $sim130$ compared to a pure CPU implementation can be achieved, largely depending on the problem size. In case our program code is integrated into an existing GPU program, speedups over a CPU implementation of up to a factor $sim165$ are possible, even for moderately sized workloads.
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