High Performance Parallel LOBPCG Method for Large Hamiltonian Derived from Hubbard Model on Multi-GPU Systems

Abstract The physical property of the Hubbard model can be understood by solving eigenvalue problem for Hamiltonian derived from model. Since is a large sparse matrix, an iteration method usually utilized problems. One effectual solvers this LOBPCG (Locally Optimal Block Preconditioned Conjugate Gradient) method. tuning strategies on GPU systems when all vectors are stored in device memory have been proposed. In research, we propose parallel multi-GPU system and some host memory. When used multi eigenpairs (eigenvalues corresponding eigenvectors), number vectors, whose size same as dimension Hamiltonian, proportional to eigenpairs. On other hand, consumption non-zero elements significantly reduced considering regular arrangement elements. Therefore, execute GPUs, transferred between needed. cost data transfer very large, also optimization it. simulation result shows that effective high performance computing.