Abstract
We present a software framework for the transparent and portable parallelization of simulations using particle-mesh methods. Particles are used to transport physical properties and a mesh is required in order to reinitialize the distorted particle locations, ensuring the convergence of the method. Field quantities are computed on the particles using fast multipole methods or by discretizing and solving the governing equations on the mesh. This combination of meshes and particles presents a challenging set of parallelization issues. The present library addresses these issues for a wide range of applications, and it enables orders of magnitude increase in the number of computational elements employed in particle methods. We demonstrate the performance and scalability of the library on several problems, including the first-ever billion particle simulation of diffusion in real biological cell geometries.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Degond, P., Mas-Gallic, S.: The weighted particle method for convection-diffusion equations. Part 1: The case of an isotropic viscosity. Math. Comput. 53(188), 485–507 (1989)
Greengard, L., Rokhlin, V.: The rapid evaluation of potential fields in three dimensions. In: Wang, D. (ed.) ADG 1996. LNCS, vol. 1360, pp. 121–141. Springer, Heidelberg (1998)
Harlow, F.H.: Particle-in-cell computing method for fluid dynamics. Methods Comput. Phys. 3, 319–343 (1964)
Hockney, R.W., Eastwood, J.W.: Computer Simulation using Particles. Institute of Physics Publishing (1988)
Sbalzarini, I.F., Walther, J.H., Bergdorf, M., Hieber, S.E., Kotsalis, E.M., Koumoutsakos, P.: PPM – a highly efficient parallel particle-mesh library for the simulation of continuum systems. J. Comput. Phys. 215(2), 566–588 (2006)
Koumoutsakos, P.: Multiscale flow simulations using particles. Annu. Rev. Fluid Mech. 37, 457–487 (2005)
Bergdorf, M., Cottet, G.H., Koumoutsakos, P.: Multilevel adaptive particle methods for convection-diffusion equations. Multiscale Model. Simul. 4(1), 328–357 (2005)
Moon, B., Saltz, J.: Adaptive runtime support for direct simulation Monte Carlo methods on distributed memory architectures. In: Proceedings of the IEEE Scalable High-Performance Computing Conference, pp. 176–183. IEEE, Los Alamitos (1994)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)
Vizing, V.G.: On an estimate of the chromatic class of a p-graph (in Russian). Diskret. Anal. 3, 25–30 (1964)
Walther, J.H.: An influence matrix particle-particle particle-mesh algorithm with exact particle-particle correction. J. Comput. Phys. 184, 670–678 (2003)
Eldredge, J.D., Leonard, A., Colonius, T.: A general deterministic treatment of derivatives in particle methods. J. Comput. Phys. 180, 686–709 (2002)
Verlet, L.: Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159(1), 98–103 (1967)
Walther, J.H., Koumoutsakos, P.: Three-dimensional particle methods for particle laden flows with two-way coupling. J. Comput. Phys. 167, 39–71 (2001)
Monaghan, J.J.: Extrapolating B splines for interpolation. J. Comput. Phys. 60, 253–262 (1985)
Alexiades, V., Amiez, G., Gremaud, P.A.: Super-time-stepping acceleration of explicit schemes for parabolic problems. Comm. Numer. Meth. Eng. 12(1), 31–42 (1996)
Williamson, J.H.: Low-storage Runge-Kutta schemes. J. Comput. Phys. 35, 48–56 (1980)
Shu, C.W., Osher, S.: Efficient implementation of essentially nonoscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988)
Cheng, H., Greengard, L., Rokhlin, V.: A fast adaptive multipole algorithm in three dimensions. J. Comput. Phys. 155, 468–498 (1999)
Chaniotis, A.K., Poulikakos, D., Koumoutsakos, P.: Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J. Comput. Phys. 182(1), 67–90 (2002)
Sbalzarini, I.F., Mezzacasa, A., Helenius, A., Koumoutsakos, P.: Effects of organelle shape on fluorescence recovery after photobleaching. Biophys. J. 89(3), 1482–1492 (2005)
Sbalzarini, I.F., Hayer, A., Helenius, A., Koumoutsakos, P.: Simulations of (an)isotropic diffusion on curved biological surfaces. Biophys. J. 90(3), 878–885 (2006)
Werder, T., Walther, J.H., Jaffe, R.L., Halicioglu, T., Koumoutsakos, P.: On the water–carbon interaction for use in molecular dynamics simulations of graphite and carbon nanotubes. J. Phys. Chem. B 107, 1345–1352 (2003)
Springel, V., Yoshida, N., White, S.D.M.: GADGET: a code for collisionless and gasdynamical cosmological simulations. New Astron 6, 79–117 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sbalzarini, I.F. et al. (2006). A Software Framework for the Portable Parallelization of Particle-Mesh Simulations. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds) Euro-Par 2006 Parallel Processing. Euro-Par 2006. Lecture Notes in Computer Science, vol 4128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11823285_76
Download citation
DOI: https://doi.org/10.1007/11823285_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37783-2
Online ISBN: 978-3-540-37784-9
eBook Packages: Computer ScienceComputer Science (R0)