Section: New Results

High performance Fast Multipole Method for N-body problems

Last year we have worked primarily on developing an efficient fast multipole method for heterogeneous architecture. Some of the accomplishments for this year include:

1. Implementation of the FMM of multicore machines using StarPU . A new parallel scheduler was developed for this purpose. We implemented a state-of-the-art OpenMP version of the code for benchmarking purposes. It was found that StarPU significantly outperforms OpenMP. Figures show the traces of an execution of the FMM algorithm with our priority scheduler for the cube (volume) and ellipsoid (surface) with 20 million particles on a 4 deca-core Intel Xeon E7-4870 machine.

2. Implementation of the FMM of heterogeneous machines (CPU+GPU) using StarPU . The FMM was also used to demonstrate the flexibility of StarPU for handling different types of processors. In particular we demonstrated in that application that StarPU can automatically select the appropriate version of a computational kernel (CPU or GPU version) and run it on the appropriate processor in order to minimize the overall runtime. Significant speed-up were obtained on heterogeneous platforms compared to multicore only processors.

These contributions have been presented in minnisymposia at the SIAM conference on Comutational Sciences and Engineering [23] , [33] in Boston and at NVIDIA GPU Technology Conference [24] . More details and results can be found in report RR-8277 [40] , our paper is accepted for publication in the SIAM Journal on Scientific Computing [11] .

Concerning dynamics dislocations (DD) kernels, an efficient formulation of the isotropic elastic far-field interactions between dislocations has been developed. This formulation is suitable for any polynomial interpolation based Fast Multipole Method (FMM) and is currently being implemented in OptiDis.

Meanwhile a much lighter and faster interpolation scheme based on a uniform grid (i.e. Lagrange interpolation) and the Fast Fourier Transform (FFT) was implemented into ScalFMM . This last feature was introduced in order to overcome the expensive cost of the Chebyshev FMM in the range of low interpolation orders (up to approx. 10). This should significantly improve the performances of the far-field computation in DD simulations where tensorial kernels are involved but only relatively low interpolation orders are required. This work is developed in the framework of Pierre Blanchard's PhD funded by ENS.