GPGPU application to the computation of Hamiltonian matrix elements between non-orthogonal Slater determinants in the Monte Carlo shell model

Togashi, Tomoaki*; Shimizu, Noritaka*; Utsuno, Yutaka   ; Abe, Takashi*; Otsuka, Takaharu*

Computing Hamiltonian matrix elements between non-orthogonal Slater determinants is often needed for nuclear-structure calculations, and it is the most time-consuming part in many cases. In this paper, we demonstrate that utilizing GPGPU is an efficient way to perform this calculation. In our earlier study, we showed that the calculation of the Hamiltonian matrix elements between non-orthogonal Slater determinants is transformed into the multiplication of matrices. This method is useful for the GPGPU calculation because of less memory access compared to the usual method. We implement the GPGPU computation in the Monte Carlo shell-model code and measure the elapsed time. The resulting performance is over 0.6 TFLOPS for the GPU that has 1.13 TFLOPS peak performance. This method is particularly effective for large-scale calculations because higher efficiency is obtained for the calculation of larger model spaces.