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Abstract: Scalable Fast Multipole Methods for Vortex Element Methods

Qi Hu, Nail A. Gumerov, Rio Yokota, Lorena Barba, Ramani Duraiswami
2012 2012 SC Companion: High Performance Computing, Networking Storage and Analysis  
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.  ...  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  ...  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.  ... 
doi:10.1109/sc.companion.2012.221 dblp:conf/sc/HuGYBD12 fatcat:bo2ypvvtszbgvclpqbucgvkseu

Parallel Implementation of Vortex Element Method on CPUs and GPUs

Kseniia Kuzmina, Ilia Marchevsky, Victoriya Moreva
2015 Procedia Computer Science  
Approximate fast multipole method usage reduces time of computations significantly: 11 times for the testmodel problem in sequential mode and 3.5 times in parallel mode for 16-cores cluster.  ...  The implementations of 2D vortex element method adapted to different types of parallel computers are considered.  ...  Fast multipole method algorithm is less-scalable, the results of the corresponding numerical experiment for the accuracy parameter of the fast method θ = 0.2 are given in Table 2 .  ... 
doi:10.1016/j.procs.2015.11.010 fatcat:fh7kgohad5cujatnjzueroxir4

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

Rio Yokota, L.A. Barba, Tetsu Narumi, Kenji Yasuoka
2013 Computer Physics Communications  
The simulations use a vortex particle method to solve the Navier-Stokes equations, with a highly parallel fast multipole method (FMM) as numerical engine, and match the current record in mesh size for  ...  The calculation time for one time step was 108 seconds for the vortex method and 154 seconds for the spectral method, under these conditions.  ...  We used three mpi processes per node to match the condition of the vortex method runs, but there is no gpu acceleration in this case.  ... 
doi:10.1016/j.cpc.2012.09.011 fatcat:zdbjrn6ga5cmlkcw7mlo77kif4

FMM-based vortex method for simulation of isotropic turbulence on GPUs, compared with a spectral method

Rio Yokota, L.A. Barba
2013 Computers & Fluids  
The fact that it uses the fast multipole method (FMM)--a hierarchical algorithm for N-body problems with highly scalable parallel implementations--as numerical engine makes it a potentially good candidate  ...  The Lagrangian vortex method offers an alternative numerical approach for direct numerical simulation of turbulence.  ...  We selected homogeneous isotropic turbulence in a periodic box as a test case, and apply a fast multipole vortex method for direct numerical simulation.  ... 
doi:10.1016/j.compfluid.2012.08.002 fatcat:5ukhafrvkndg3gynpey5ygq4ey

Linear-Time Smoke Animation with Vortex Sheet Meshes [article]

Tyson Brochu, Todd Keeler, Robert Bridson
2012 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '04  
The simulation itself runs in time linear to the number of triangles thanks to the use of a well-conditioned integral equation treatment together with a Fast Multipole Method for linear-time summations  ...  Our fundamental representation is a closed triangle mesh surface dividing space between clear air and a uniformly smoky region, on which we compute vortex sheet dynamics to accurately solve inviscid buoyant  ...  layer potential on a sphere using BiCGSTAB, computing the matrix multiply with both the direct method and Fast Multipole Method.  ... 
doi:10.2312/sca/sca12/087-095 fatcat:pmcxni5orba57pykgq7shtq3d4

A parallel hierarchical-element method for contour dynamics simulations

R.M. Schoemaker, P.C.A. de Haas, H.J.H. Clercx, R.M.M. Mattheij
2005 Computers & Fluids  
Several applications require the use of a hierarchical-element method (HEM), a modified version of the classical contour dynamics scheme by applying a fast multipole method, in order to accelerate the  ...  Many two-dimensional incompressible inviscid vortex flows can be simulated with high efficiency by means of the contour dynamics method.  ...  The next section explains the contour dynamics method, the fast multipole technique and the hierarchical-element method for contour dynamics in a concise manner.  ... 
doi:10.1016/j.compfluid.2004.09.007 fatcat:3egwvbnly5glhfmehfht6zjfpu

A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems

Rio Yokota, Lorena A Barba
2012 The international journal of high performance computing applications  
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star.  ...  Parallel scalability was studied in both strong and weak scaling.  ...  He has worked on the implementation of fast N-body algorithms on special-purpose machines such as MD-GRAPE-3, and then on GPUs after CUDA was released, and on vortex methods for fluids simulation.  ... 
doi:10.1177/1094342011429952 fatcat:4m5wtfvbbvbfxco73bgo5dtvc4

Removing the Barrier to Scalability in Parallel FMM [article]

Matthew G. Knepley
2010 arXiv   pre-print
The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990].  ...  We show that this potential bottleneck can be eliminated by overlapping multipole and local expansion computations with direct kernel evaluations on the finest level grid.  ...  Introduction In [1] , Greengard and Gropp give the seminal complexity analysis for the parallel Fast Multipole Method (FMM) [2] .  ... 
arXiv:1008.2410v1 fatcat:jsogit55pbazpbymzasopvfyhe

Scalable fast multipole methods on distributed heterogeneous architectures

Qi Hu, Nail A. Gumerov, Ramani Duraiswami
2011 Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '11  
We fundamentally reconsider implementation of the Fast Multipole Method (FMM) on a computing node with a heterogeneous CPU-GPU architecture with multicore CPU(s) and one or more GPU accelerators, as well  ...  Careful analysis of the FMM is performed to distribute work optimally between the multicore CPUs and the GPU accelerators.  ...  Fast multipole method and scalability The FMM, because of its linear complexity, allows the algorithm size to scale well, if it were implementable efficiently on new architectures.  ... 
doi:10.1145/2063384.2063432 dblp:conf/sc/HuGD11 fatcat:dxmswho42vhp7pm5klcymnebx4

Biomolecular electrostatics using a fast multipole BEM on up to 512 gpus and a billion unknowns

Rio Yokota, Jaydeep P. Bardhan, Matthew G. Knepley, L.A. Barba, Tsuyoshi Hamada
2011 Computer Physics Communications  
The algorithmic acceleration is achieved with the fast multipole method (FMM) in conjunction with a boundary element method (BEM) formulation of the continuum electrostatic model, as well as the BIBEE  ...  The parallel scalability of the software was studied in a cluster at the Nagasaki Advanced Computing Center, using 128 nodes, each with 4 GPUs.  ...  Fast multipole method The fast multipole method is an algorithm that accelerates the computations required in N -body problems, which are expressed as a sum of the form f (y j ) = N i=1 c i K(y j , x i  ... 
doi:10.1016/j.cpc.2011.02.013 fatcat:62eidsyjknf5fhfmq266gybk6u

Dynamic Autotuning of Adaptive Fast Multipole Methods on Hybrid Multicore CPU and GPU Systems

Marcus Holm, Stefan Engblom, Anders Goude, Sverker Holmgren
2014 SIAM Journal on Scientific Computing  
We discuss an implementation of adaptive fast multipole methods targeting hybrid multicore CPU- and GPU-systems.  ...  From previous experiences with the computational profile of our version of the fast multipole algorithm, suitable parts are off-loaded to the GPU, while the remaining parts are threaded and executed concurrently  ...  Fast multipole methods Since first presented in [5, 16] , Fast Multipole Methods (FMMs) have remained a crucial tool for fast evaluation of pairwise interactions of the type Φ(x i ) = N j=1,j =i G(x i  ... 
doi:10.1137/130943595 fatcat:zvahv4it5bfdlkpytywhkt7uyi

PetFMM-A dynamically load-balancing parallel fast multipole library

Felipe A. Cruz, Matthew G. Knepley, L. A. Barba
2010 International Journal for Numerical Methods in Engineering  
To this last class belongs the well-known fast multipole method (FMM), which offers O(N) complexity.  ...  Fast algorithms for the computation of N-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods.  ...  Overview of the Fast Multipole Method algorithm The fast multipole method (fmm) is an algorithm which accelerates computations of the form: f (y j ) = N i=1 c i K(y j , x i ) (1) representing a field value  ... 
doi:10.1002/nme.2972 fatcat:phm6w43kxzfmrjntoroyzuo7wy

A PPPM fast summation method for fluids and beyond

Xinxin Zhang, Robert Bridson
2014 ACM Transactions on Graphics  
The naive direct summation of the kernel function over all particles scales quadratically, rendering it too slow for large problems, while the optimal Fast Multipole Method has drastic implementation complexity  ...  We demonstrate the power of PPPM with a new vortex particle smoke solver, which features a vortex segment-approach to the stretching term, potential flow to enforce no-stick solid boundaries on arbitrary  ...  Foremost among these is the Fast Multipole Method (FMM) [Greengard and Rokhlin 1987] , which can reduce the cost from O(M N ) to O(M + N ).  ... 
doi:10.1145/2661229.2661261 fatcat:q2qbtn6hirfl5hv6fqauo6cxkm

Scalable Distributed Fast Multipole Methods

Qi Hu, Nail A. Gumerov, Ramani Duraiswami
2012 2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software and Systems  
The Fast Multipole Method (FMM) allows O(N ) evaluation to any arbitrary precision of N -body interactions that arises in many scientific contexts.  ...  While impressive performance was reported, the algorithms did not demonstrate complete weak or strong scalability.  ...  , vortex methods and statistics.  ... 
doi:10.1109/hpcc.2012.44 dblp:conf/hpcc/HuGD12 fatcat:urstmdeybjbqdb7p77252f2npq

Billion vortex particle direct numerical simulations of aircraft wakes

Philippe Chatelain, Alessandro Curioni, Michael Bergdorf, Diego Rossinelli, Wanda Andreoni, Petros Koumoutsakos
2008 Computer Methods in Applied Mechanics and Engineering  
The method exhibits excellent scalability up to 16k BG/L nodes.  ...  We present the Direct Numerical Simulations of high Reynolds numbers aircraft wakes employing vortex particle methods.  ...  We note that transverse unbounded conditions can be achieved by using hybrid Fast Multipole-VIC methods [13, 14] but also with fast convolutions in Fourier space [19] ; this extension is an area of  ... 
doi:10.1016/j.cma.2007.11.016 fatcat:dzozs5rll5gjhnantxmldxtrw4
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