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.

[1]  Fernando Obelleiro Basteiro,et al.  HP-FASS: a hybrid parallel fast acoustic scattering solver , 2011, Int. J. Comput. Math..

[2]  T. Eibert,et al.  A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals , 2005, IEEE Transactions on Antennas and Propagation.

[3]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[4]  Message Passing Interface Forum MPI: A message - passing interface standard , 1994 .

[5]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[6]  Ramani Duraiswami,et al.  CHAPTER 5 – Fast Multipole Methods , 2004 .

[7]  V. Rokhlin Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions , 1993 .

[8]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[9]  Andrew Thall,et al.  Fast Mersenne prime testing on the GPU , 2011, GPGPU-4.

[10]  Message P Forum,et al.  MPI: A Message-Passing Interface Standard , 1994 .

[11]  Ramani Duraiswami,et al.  Data Structures, Optimal Choice of Parameters, and Complexity Results for Generalized Multilevel Fast Multipole Methods in $d$ Dimensions , 2003 .

[12]  Michael Mikolajczak,et al.  Designing And Building Parallel Programs: Concepts And Tools For Parallel Software Engineering , 1997, IEEE Concurrency.

[13]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[14]  Jiming Song,et al.  Multilevel fast‐multipole algorithm for solving combined field integral equations of electromagnetic scattering , 1995 .

[15]  José Ranilla,et al.  Acoustic scattering solver based on single level FMM for multi-GPU systems , 2012, J. Parallel Distributed Comput..

[16]  Richard W. Vuduc,et al.  A massively parallel adaptive fast-multipole method on heterogeneous architectures , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[17]  Wilfred Pinfold,et al.  Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis , 2009, HiPC 2009.

[18]  Ramani Duraiswami,et al.  Fast multipole methods on graphics processors , 2008, J. Comput. Phys..

[19]  José Ranilla,et al.  A GPGPU solution of the FMM near interactions for acoustic scattering problems , 2011, The Journal of Supercomputing.

[20]  John D. Owens,et al.  GPU Computing , 2008, Proceedings of the IEEE.

[21]  V. Rokhlin Rapid Solution of Integral Equations of Scattering Theory , 1990 .