GPU-Based Parallelization of Kernel Polynomial Method for Solving LDOS

Materials science brings innovations for creating novel human activity by discovering new materials with various functionalities such as semiconductors, superconductors, and ferromagnets. In condensed matter physics, these different characteristics of materials are understood microscopically by different behavior of electrons, which can be eagerly simulated on high power computer. The simulation is performed in the quantum level focusing on the behavior of electrons around atoms which form lattice of various shapes. The main task in the simulation thus corresponds to diagonalize a Hamiltonian matrix for the lattice system and evaluate the electronic density of energy states. The local density of states (LDOS) is one of the most fundamental quantities to investigate materials properties including electronic conductivity and localization. Kernel Polynomial Method (KPM) is one of the major efficient methods for diagonalizaing Hamiltonian matrix, which decreases the complexity significantly compared to the full diagonalization method. However, it is hard to have a large speedup in a computing resource with multicore CPUs due to the bottleneck of the memory interface. This paper focuses on improving the performance applying GPU to the LDOS calculation using the large bandwidth of GPUs. This paper shows the parallel design and its implementation of LDOS algorithm on a single GPU and also extended on a GPU cluster. According to the performance evaluation, we confirm that the GPU-based parallelization applying a GPU cluster computer achieves the higher performance equivalent to about 24 times larger number of CPU cores.