Scalable fast multipole methods for vortex element methods

Hu, Qi; Gumerov, Nail A.; Yokota, Rio; Barba, Lorena A.; Duraiswami, Ramani

Scalable fast multipole methods for vortex element methods

Type

Conference Paper

Authors

Hu, Qi
Gumerov, Nail A.
Yokota, Rio

Barba, Lorena A.
Duraiswami, Ramani

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center

Date

2012-11

Abstract

We use a particle-based method to simulate incompressible flows, where the Fast Multipole Method (FMM) is used to accelerate the calculation of particle interactions. The most time-consuming kernelsâ'the Biot-Savart equation and stretching term of the vorticity equationâ'are mathematically reformulated so that only two Laplace scalar potentials are used instead of six, while automatically ensuring divergence-free far-field computation. Based on this formulation, and on our previous work for a scalar heterogeneous FMM algorithm, we develop a new FMM-based vortex method capable of simulating general flows including turbulence on heterogeneous architectures, which distributes the work between multi-core CPUs and GPUs to best utilize the hardware resources and achieve excellent scalability. The algorithm also uses new data structures which can dynamically manage inter-node communication and load balance efficiently but with only a small parallel construction overhead. This algorithm can scale to large-sized clusters showing both strong and weak scalability. Careful error and timing trade-off analysis are also performed for the cutoff functions induced by the vortex particle method. Our implementation can perform one time step of the velocity+stretching for one billion particles on 32 nodes in 55.9 seconds, which yields 49.12 Tflop/s. © 2012 IEEE.

Citation

Qi Hu, Nail A. Gumerov, Rio Yokota, Lorena Barba, & Ramani Duraiswami. (2012). Abstract: Scalable Fast Multipole Methods for Vortex Element Methods. 2012 SC Companion: High Performance Computing, Networking Storage and Analysis. doi:10.1109/sc.companion.2012.221