Scalable fast multipole methods for vortex element methods

Handle URI:
http://hdl.handle.net/10754/564623
Title:
Scalable fast multipole methods for vortex element methods
Authors:
Hu, Qi; Gumerov, Nail A.; Yokota, Rio ( 0000-0001-7573-7873 ) ; Barba, Lorena A.; Duraiswami, Ramani
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.
KAUST Department:
Extreme Computing Research Center
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2012 SC Companion: High Performance Computing, Networking Storage and Analysis
Conference/Event name:
2012 SC Companion: High Performance Computing, Networking Storage and Analysis, SCC 2012
Issue Date:
Nov-2012
DOI:
10.1109/SC.Companion.2012.221
Type:
Conference Paper
ISBN:
9780769549569
Appears in Collections:
Conference Papers; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorHu, Qien
dc.contributor.authorGumerov, Nail A.en
dc.contributor.authorYokota, Rioen
dc.contributor.authorBarba, Lorena A.en
dc.contributor.authorDuraiswami, Ramanien
dc.date.accessioned2015-08-04T07:05:22Zen
dc.date.available2015-08-04T07:05:22Zen
dc.date.issued2012-11en
dc.identifier.isbn9780769549569en
dc.identifier.doi10.1109/SC.Companion.2012.221en
dc.identifier.urihttp://hdl.handle.net/10754/564623en
dc.description.abstractWe 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.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectfast multipole methoden
dc.subjectheterogeneous algorithmen
dc.subjectvortex methodsen
dc.subjectGPUen
dc.titleScalable fast multipole methods for vortex element methodsen
dc.typeConference Paperen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journal2012 SC Companion: High Performance Computing, Networking Storage and Analysisen
dc.conference.date10 November 2012 through 16 November 2012en
dc.conference.name2012 SC Companion: High Performance Computing, Networking Storage and Analysis, SCC 2012en
dc.conference.locationSalt Lake City, UTen
dc.contributor.institutionUniversity of Maryland Institute for Advanced Computer Studies (UMIACS), Fantalgo LLC, Elkridge, MD, United Statesen
dc.contributor.institutionDepartment of Computer Science, University of Maryland, College Park, United Statesen
dc.contributor.institutionFantalgo LLC, Elkridge, MD, United Statesen
dc.contributor.institutionMechanical Engineering Department, Boston University, United Statesen
kaust.authorYokota, Rioen
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