Single level fast multipole method on GPU cluster for electromagnetic problems

Fast Multipole Method (FMM) is a mathematical technique which was developed to seek rapid solutions to integral equations of scattering for Helmholtz problems. For scattering problems, the integral equation is discretized into a matrix equation by the method of moments (MoM). The resultant equation is then typically solved by the direct LU, or an iterative method which requires O(N3) or O(N2) floating point operations respectively. However, if FMM is implemented, the complexity is reduced to O(N3/2). Moreover, the multilevel fast multipole algorithm (MLFMA) which is a multistage FMM can further reduce the complexity to O(NlogN). These methods are promising for providing a path to large scale computing in electromagnetics.In this paper, the exploitation of an HPC GPU cluster to implement single level fast multipole method for large scale scattering problems is investigated. The NVIDIA's Compute Unified Device Architecture (CUDA) and MVAPICH2 programming environments are utilized on a 13-node cluster equipped with GPUs and interconnected through a high bandwidth, low latency Infiniband network.