High Performance Eigenvalue Solver in Exact-diagonalization Method for Hubbard Model on CUDA GPU
Yamada Susumu, Toshiyuki Imamura, Masahiko Machida · Advances in parallel computing · 2016
The graphics processing unit (GPU) is an excellent accelerator and it can realize speedup with appropriate tuning. In this paper, we present a tuning technique for the exact diagonalization method, which is widely used as a numerical tool to obtain the ground state (the smallest eigenvalue and the corresponding eigenvector) of the Hamiltonian derived from the Hubbard model, on the GPU architecture. Since the Hamiltonian is a sparse matrix, an iteration method is used for solving the eigenvalue problems. We mainly tune the code for the multiplication of the Hamiltonian and a vector, which is the most time-consuming operation in the iteration method. The numerical test shows that the tuned code is faster than the one with using the routine “cusparseDcsrmm” of cuSPARSE library. Moreover, the tuned method on NVIDIA Tesla M2075 achieves about 3× speedup as compared with the thread-parallelized code on six threads of Intel Xeon 5650 for the multiplication.