Single Level Fast Multipole Method Research Articles

Improving the FMM performance using optimal group size on heterogeneous system architectures

The fast multipole method (FMM) is commonly used to speed-up the time to solution of a wide diversity of N-body type problems. To use the FMM, the elements that constitute the geometry of the problem are clustered into groups of a given size (D) that may deeply vary the time to solution of the FMM. The optimal value of D, in the sense of minimizing the time cost, is unknown beforehand and it depends on several factors. Nevertheless, during the solver setup, it is possible to produce clusters of varying size D and to estimate the time to solution associated with each D. In this paper, we use octree structures to efficiently perform clustering and time cost estimation to find the optimal group size for the FMM implementations on a heterogeneous architecture. In addition, two different frameworks have been analyzed: single-level FMM and fast Fourier transform FMM (FMM-FFT). We found that the sensitivity of the time cost to the parameter D depends on factors, such as the problem size or the implementation of the FMM framework. Moreover, we observed that the time cost may be conspicuously reduced if a proper D is employed.

Parallelizing Fast Multipole Method for Large-Scale Electromagnetic Problems Using GPU Clusters

This letter investigates the solution of large-scale electromagnetic problems by using the single-level Fast Multipole Method (FMM). Problems of large scale require high computational capability that cannot be accommodated using conventional computing systems. We investigate a parallel implementation of FMM on a 13-node graphics processing unit (GPU) cluster that populates Nvidia Tesla M2090 GPUs. The implementation details and the performance achievements in terms of accuracy, speedup, and scalability are discussed. The experimental results demonstrate that our FMM implementation on GPUs is much faster than (up to 700 ×) that of the CPU implementation. Moreover, the scalability of the GPU implementation is very close to the theoretical linear expectations.

Parallelization of the FMM on distributed-memory GPGPU systems for acoustic-scattering prediction

In this work, we carry out the parallelization of the single level Fast Multipole Method (FMM) for solving acoustic-scattering problems (using the Helmholtz equation) on distributed-memory GPGPU systems. With the aim of enlarging the scope of feasible simulations, the presented solution combines the techniques developed for our distributed-memory CPU solver with our shared-memory GPGPU solver. The performance of the developed solution is proved using two different GPGPU clusters: the first one consists of two workstations with NVIDIA GTX 480 GPUs linked by a Gigabit Ethernet network, and the second one comprises four nodes with NVIDIA Tesla M2090 GPUs linked by an Infiniband network.

Accelerated boundary element method for diffuse optical imaging

The boundary element method (BEM) is a useful tool in diffuse optical imaging (DOI) when modelling large optical regions whose parameters are piecewise constant, but are computationally expensive. We present here an acceleration technique, the single-level fast multipole method, for a highly lossy medium. The enhanced practicability of the BEM in DOI is demonstrated through test examples on single-layer problems, where order of magnitude reduction factors on solution time are achieved and on a realistic three-layer model of the neonatal head. Our experimental results agree very closely with theoretical predictions of computational complexity.

Acoustic scattering solver based on single level FMM for multi-GPU systems

In this paper, we present a heterogeneous parallel solver of a high frequency single level Fast Multipole Method (FMM) for the Helmholtz equation applied to acoustic scattering. The developed solution uses multiple GPUs to tackle the compute bound steps of the FMM (aggregation, disaggregation, and near interactions) while the CPU handles a memory bound step (translation) using OpenMP. The proposed solver performance is measured on a workstation with two GPUs (NVIDIA GTX 480) and is compared with that of a distributed memory solver run on a cluster of 32 nodes (HP BL465c) with an Infiniband network. Some energy efficiency results are also presented in this work.