Abstract
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.
Similar content being viewed by others
References
Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. Dover, New York
Burton AJ, Miller GF (1971) The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc R Soc Lond Ser A, Math Phys Sci 323(1553):201–210
Coifman R, Rokhlin V, Wandzura S (1993) The fast multipole method for the wave equation: a pedestrian prescription. IEEE Antennas Propag Mag 35(3):7–12
Eibert TF (2005) A diagonalized multilevel fast multipole method with spherical harmonics expansion of the κ-space integrals. IEEE Trans Antennas Propag 53(2):814–817
Foster I (1995) Designing and building parallel programs: concepts and tools for parallel software engineering. Addison-Wesley, Reading
GPGPU.org (2011) General-purpose computation on Graphics Processing Units. Available online at: http://gpgpu.org/
Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comput Phys 73:325–348
Gumerov NA, Duraiswami R, Borovikov EA (2003) Data structures, optimal choice of parameters, and complexity results for generalized multilevel fast multipole methods in d dimensions. Technical reports from UMIACS
Gumerov NA, Duraiswami R (2008) Fast multipole methods on graphics processors. J Comput Phys 227(18):8290–8313
Lashuk I, Chandramowlishwaran A, Langston H, Nguyen T, Sampath R, Shringarpure A, Vuduc R, Ying L, Zorin D, Biros G (2009) A massively parallel adaptive fast-multipole method on heterogeneous architectures. In: Proceedings of the conference on high performance computing networking, storage and analysis (SC ’09), pp 1–12
López-Fernández JA, Portugués ML, Taboada JM, Rice HJ, Obelleiro F (2011) HP-FASS: a hybrid parallel fast acoustic scattering solver. Int J Comput Math 88(9):1960–1968
López-Portugués M, López-Fernández JA, Rodríguez-Campa A, Ranilla J (2011) A GPGPU solution of the FMM near interactions for acoustic scattering problems. J Supercomput 58(3):283–291
López-Portugués M, López-Fernández JA, Menéndez-Canal J, Rodríguez-Campa A, Ranilla J (2011) Acoustic scattering solver based on single level FMM for Multi-GPU systems. J Parallel Distrib Comput. doi:10.1016/j.jpdc.2011.07.013
Message Passing Interface Forum (2009) MPI: A message-passing interface standard, Rel 2.2. Available online at: http://www.mpi-forum.org/
Microway Incorporated (2011) NVIDIA MD SimCluster test drive program. Available online at: http://www.microway.com/
The OpenMP ARB (2004) OpenMP. Available online at: http://www.openmp.org/
Owens JD, Houston M, Luebke D, Green S, Stone JE, Phillips JC (2008) GPU computing. Proc IEEE 96(5):879–899
Rokhlin V (1990) Rapid solution of integral equations of scattering theory in two dimension. J Comput Phys 86(2):424–439
Rokhlin V (1993) Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Appl Comput Harmon Anal 1(1):82–93
Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869
Song J, Chew W (1995) Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microw Opt Technol Lett 10(1):14–19
Wu TW (2000) Boundary element acoustics, advances in boundary elements. WIT Press, Southampton
Acknowledgements
This work has been partially supported by “Ministerio de Ciencia e Innovación” from Spain/FEDER under the research projects TEC2011-24492/TEC (iSCAT) and TIN2010-14971, and by “Gobierno del Principado de Asturias” (PCTI)/ FEDER under project PC10-06. The Airbus A300 series geometry has been provided by the research project GRD1-2001-40147 financed by the European Union. Financial support (grant: UNOV-10-BECDOC) given by the University of Oviedo is acknowledged. Finally, many thanks are due to Microway Incorporated by the chance of using their Tesla MD SimCluster.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
López-Portugués, M., López-Fernández, J.A., Ranilla, J. et al. Parallelization of the FMM on distributed-memory GPGPU systems for acoustic-scattering prediction. J Supercomput 64, 17–27 (2013). https://doi.org/10.1007/s11227-012-0786-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-012-0786-6