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Volumn 65, Issue 8, 2005, Pages 949-962

Parallel multigrid summation for the N-body problem

Author keywords

Fast electrostatic solvers; Multigrid summation; Parallel N body solvers; Particle mesh Ewald

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER OPERATING SYSTEMS; COMPUTER SIMULATION; COMPUTER SOFTWARE; DNA; ELECTROSTATICS; GRAVITATIONAL EFFECTS; PROTEINS;

EID: 20444461136     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpdc.2005.03.006     Document Type: Article
Times cited : (31)

References (63)
  • 1
    • 0342625956 scopus 로고
    • Multilevel methods for fast solution of N-body and hybrid systems
    • Birkhäuser Verlag, Basel
    • D.S. Balsara, A. Brandt, Multilevel methods for fast solution of N -body and hybrid systems, in: International Series of Numerical Mathematics, vol. 98, Birkhäuser Verlag, Basel, 1991, pp. 131-142.
    • (1991) International Series of Numerical Mathematics , vol.98 , pp. 131-142
    • Balsara, D.S.1    Brandt, A.2
  • 2
    • 33846349887 scopus 로고
    • A hierarchical O(N log N) force-calculation algorithm
    • J. Barnes, and P. Hut A hierarchical O (N log N) force-calculation algorithm Nature 324 1986 446 449
    • (1986) Nature , vol.324 , pp. 446-449
    • Barnes, J.1    Hut, P.2
  • 3
    • 0035449971 scopus 로고    scopus 로고
    • Optimized particle-mesh Ewald/multiple-time step integration for molecular dynamics simulations
    • P.F. Batcho, D.A. Case, and T. Schlick Optimized particle-mesh Ewald/multiple-time step integration for molecular dynamics simulations J. Chem. Phys. 115 9 2001 4003 4018
    • (2001) J. Chem. Phys. , vol.115 , Issue.9 , pp. 4003-4018
    • Batcho, P.F.1    Case, D.A.2    Schlick, T.3
  • 4
    • 0041295916 scopus 로고
    • Grid-multipole calculations
    • C.L. Berman Grid-multipole calculations SIAM J. Sci. Comput. 16 1995 1082 1091
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1082-1091
    • Berman, C.L.1
  • 5
    • 0000316648 scopus 로고    scopus 로고
    • Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics
    • T. Bishop, R.D. Skeel, and K. Schulten Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics J. Comp. Chem. 18 14 1997 1785 1791
    • (1997) J. Comp. Chem. , vol.18 , Issue.14 , pp. 1785-1791
    • Bishop, T.1    Skeel, R.D.2    Schulten, K.3
  • 8
    • 0242388520 scopus 로고    scopus 로고
    • Tree-Particle Mesh: An adaptive efficient and parallel code for collisionless cosmological simulation
    • P. Bode, and J.P. Ostriker Tree-Particle Mesh: an adaptive efficient and parallel code for collisionless cosmological simulation Astrophys. J. (Suppl. Series) 145 1 2003 1 13
    • (2003) Astrophys. J. (Suppl. Series) , vol.145 , Issue.1 , pp. 1-13
    • Bode, P.1    Ostriker, J.P.2
  • 9
    • 0026413037 scopus 로고
    • Multilevel computations of integral transforms and particle interactions with oscillatory kernels
    • A. Brandt Multilevel computations of integral transforms and particle interactions with oscillatory kernels Comput. Phys. Commun. 65 1-3 1991 24 38
    • (1991) Comput. Phys. Commun. , vol.65 , Issue.1-3 , pp. 24-38
    • Brandt, A.1
  • 11
    • 28144464582 scopus 로고
    • Multilevel matrix multiplication and fast solution of integral equations
    • A. Brandt, and A.A. Lubrecht Multilevel matrix multiplication and fast solution of integral equations J. Comput. Phys. 90 1990 348 370
    • (1990) J. Comput. Phys. , vol.90 , pp. 348-370
    • Brandt, A.1    Lubrecht, A.A.2
  • 12
    • 0033708935 scopus 로고    scopus 로고
    • Semicoarsening multigrid on distributed memory machines
    • P.N. Brown, R.D. Falgout, and J.E. Jones Semicoarsening multigrid on distributed memory machines SIAM J. Sci. Comput. 21 5 2000 1823 1834
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.5 , pp. 1823-1834
    • Brown, P.N.1    Falgout, R.D.2    Jones, J.E.3
  • 14
    • 20444473641 scopus 로고    scopus 로고
    • MDSimAid: Automatic parameter optimization in fast electrostatic algorithms
    • M.S. Crocker, S.S. Hampton, T. Matthey, J.A. Izaguirre, MDSimAid: Automatic parameter optimization in fast electrostatic algorithms, J. Comp. Chem. 26 (10) (2005) 1021-1031.
    • (2005) J. Comp. Chem. , vol.26 , Issue.10 , pp. 1021-1031
    • Crocker, M.S.1    Hampton, S.S.2    Matthey, T.3    Izaguirre, J.A.4
  • 16
    • 33846823909 scopus 로고
    • Particle mesh Ewald: An N log(N) method for Ewald sums in large systems
    • T. Darden, D. York, and L. Pedersen Particle mesh Ewald: An N log (N) method for Ewald sums in large systems J. Chem. Phys. 98 12 1993 10089 10092
    • (1993) J. Chem. Phys. , vol.98 , Issue.12 , pp. 10089-10092
    • Darden, T.1    York, D.2    Pedersen, L.3
  • 17
    • 0037054401 scopus 로고    scopus 로고
    • A hierarchical O(N) force calculation algorithm
    • W. Dehnen A hierarchical O(N) force calculation algorithm J. Chem. Phys. 179 1 2002 27 42
    • (2002) J. Chem. Phys. , vol.179 , Issue.1 , pp. 27-42
    • Dehnen, W.1
  • 18
    • 0001786236 scopus 로고
    • Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants
    • S.W. de Leeuw, J.W. Perram, and E.R. Smith Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants Proc. R. Soc. Lond. A 373 1980 27 56
    • (1980) Proc. R. Soc. Lond. a , vol.373 , pp. 27-56
    • De Leeuw, S.W.1    Perram, J.W.2    Smith, E.R.3
  • 19
    • 22244433235 scopus 로고    scopus 로고
    • How to mesh up Ewald sums. I. a theoretical and numerical comparison of various particle mesh routines
    • M. Deserno, and C. Holm How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines J. Chem. Phys. 109 18 1998 7678 7693
    • (1998) J. Chem. Phys. , vol.109 , Issue.18 , pp. 7678-7693
    • Deserno, M.1    Holm, C.2
  • 20
    • 0034270925 scopus 로고    scopus 로고
    • An Ewald summation based multipole method
    • Z.H. Duan, and R. Krasny An Ewald summation based multipole method J. Chem. Phys. 113 9 2000 3492 3495
    • (2000) J. Chem. Phys. , vol.113 , Issue.9 , pp. 3492-3495
    • Duan, Z.H.1    Krasny, R.2
  • 21
    • 0000687899 scopus 로고    scopus 로고
    • An adaptive treecode for computing nonbonded potential energy in classical molecular systems
    • Z.H. Duan, and R. Krasny An adaptive treecode for computing nonbonded potential energy in classical molecular systems J. Comp. Chem. 22 2 2001 184 195
    • (2001) J. Comp. Chem. , vol.22 , Issue.2 , pp. 184-195
    • Duan, Z.H.1    Krasny, R.2
  • 22
    • 33645961739 scopus 로고
    • A smooth particle mesh Ewald method
    • U. Essmann, L. Perera, and M.L. Berkowitz A smooth particle mesh Ewald method J. Chem. Phys. 103 19 1995 8577 8593
    • (1995) J. Chem. Phys. , vol.103 , Issue.19 , pp. 8577-8593
    • Essmann, U.1    Perera, L.2    Berkowitz, M.L.3
  • 23
    • 84977266737 scopus 로고
    • Die Berechnung optischer und elektrostatischer Gitterpotentiale
    • P. Ewald Die Berechnung optischer und elektrostatischer Gitterpotentiale Ann. Phys. 64 1921 253 287
    • (1921) Ann. Phys. , vol.64 , pp. 253-287
    • Ewald, P.1
  • 24
    • 0028043019 scopus 로고
    • Optimisation of the Ewald sum for large systems
    • D. Fincham Optimisation of the Ewald sum for large systems Mol. Simul. 13 1994 1 9
    • (1994) Mol. Simul. , vol.13 , pp. 1-9
    • Fincham, D.1
  • 26
  • 27
    • 0022683543 scopus 로고
    • On the structure of parallelism in a highly concurrent PDE solver
    • D. Gannon, and J. Vanrosendale On the structure of parallelism in a highly concurrent PDE solver J. Parallel Distrib. Comput. 3 1 1986 106 135
    • (1986) J. Parallel Distrib. Comput. , vol.3 , Issue.1 , pp. 106-135
    • Gannon, D.1    Vanrosendale, J.2
  • 28
    • 0032097210 scopus 로고    scopus 로고
    • Scalable parallel formulations of the Barnes-Hut method for N-body simulations
    • A. Grama, V. Kumar, and A. Sameh Scalable parallel formulations of the Barnes-Hut method for N -body simulations J. Parallel Comput. 24 5-6 1998 797 822
    • (1998) J. Parallel Comput. , vol.24 , Issue.5-6 , pp. 797-822
    • Grama, A.1    Kumar, V.2    Sameh, A.3
  • 29
    • 0033678471 scopus 로고    scopus 로고
    • Improving error bounds for multipole-based treecodes
    • A. Grama, V. Sarin, and A. Sameh Improving error bounds for multipole-based treecodes SIAM J. Sci. Comput. 21 5 2000 1790 1803
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.5 , pp. 1790-1803
    • Grama, A.1    Sarin, V.2    Sameh, A.3
  • 31
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulation
    • L. Greengard, and V. Rokhlin A fast algorithm for particle simulation J. Comput. Phys. 73 1987 325 348
    • (1987) J. Comput. Phys. , vol.73 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 32
    • 0032648001 scopus 로고    scopus 로고
    • Parallel multigrid in an adaptive PDE solver based on hashing and space-filled curves
    • M. Griebel, and G. Zumbusch Parallel multigrid in an adaptive PDE solver based on hashing and space-filled curves J. Parallel Comput. 25 7 1999 827 843
    • (1999) J. Parallel Comput. , vol.25 , Issue.7 , pp. 827-843
    • Griebel, M.1    Zumbusch, G.2
  • 33
    • 0000617850 scopus 로고
    • Structure and Mandelung energy of spherical Coulomb crystals
    • R.H. Hasse, and V.V. Avilov Structure and Mandelung energy of spherical Coulomb crystals Phys. Rev. A 44 7 1991 4506 4515
    • (1991) Phys. Rev. a , vol.44 , Issue.7 , pp. 4506-4515
    • Hasse, R.H.1    Avilov, V.V.2
  • 36
    • 0000504254 scopus 로고
    • A multiple-time-step molecular dynamics algorithm for macromolecules
    • D.D. Humphreys, R.A. Friesner, and B.J. Berne A multiple-time-step molecular dynamics algorithm for macromolecules J. Phys. Chem. 98 27 1994 6885 6892
    • (1994) J. Phys. Chem. , vol.98 , Issue.27 , pp. 6885-6892
    • Humphreys, D.D.1    Friesner, R.A.2    Berne, B.J.3
  • 37
    • 0024523877 scopus 로고
    • Defined apolipoprotein A-I conformations in reconstituted high density lipoprotein discs
    • A. Jonas, K.E. Kezdy, and J.H. Wald Defined apolipoprotein A-I conformations in reconstituted high density lipoprotein discs J. Biol. Chem. 264 1989 4818 4824
    • (1989) J. Biol. Chem. , vol.264 , pp. 4818-4824
    • Jonas, A.1    Kezdy, K.E.2    Wald, J.H.3
  • 40
    • 0030188166 scopus 로고    scopus 로고
    • A multipole-based algorithm for efficient calculation of forces and potentials in macroscopic periodic assemblies of particles
    • C.G. Lambert, T.A. Darden, and J.A. Board A multipole-based algorithm for efficient calculation of forces and potentials in macroscopic periodic assemblies of particles J. Comput. Phys. 126 2 1996 274 287
    • (1996) J. Comput. Phys. , vol.126 , Issue.2 , pp. 274-287
    • Lambert, C.G.1    Darden, T.A.2    Board, J.A.3
  • 41
    • 0030257515 scopus 로고    scopus 로고
    • Parallelism in multigrid methods: How much is too much?
    • L.R. Matheson, and R.E. Tarjan Parallelism in multigrid methods: How much is too much? Internat. J. Parallel Program. 24 5 1996 397 432
    • (1996) Internat. J. Parallel Program. , vol.24 , Issue.5 , pp. 397-432
    • Matheson, L.R.1    Tarjan, R.E.2
  • 44
    • 0345330826 scopus 로고    scopus 로고
    • Coulomb bi-crystals of species with identical charge-to-mass ratios
    • T. Matthey, J.P. Hansen, and M. Drewsen Coulomb bi-crystals of species with identical charge-to-mass ratios Phys. Rev. Lett. 91 16 2003 165001
    • (2003) Phys. Rev. Lett. , vol.91 , Issue.16 , pp. 165001
    • Matthey, T.1    Hansen, J.P.2    Drewsen, M.3
  • 45
    • 0031636785 scopus 로고    scopus 로고
    • The full domain partition approach to distributing adaptive grids
    • W.F. Mitchell The full domain partition approach to distributing adaptive grids Appl. Numer. Math. 26 8 1998 265 275
    • (1998) Appl. Numer. Math. , vol.26 , Issue.8 , pp. 265-275
    • Mitchell, W.F.1
  • 46
    • 0000518787 scopus 로고    scopus 로고
    • Parallel transient dynamics simulations: Algorithms for contact detection and smoothed particle hydrodynamics
    • S. Plimpton, S. Attaway, B. Hendrickson, J. Swegle, C. Vaughan, and D. Gardner Parallel transient dynamics simulations: Algorithms for contact detection and smoothed particle hydrodynamics J. Parallel Distrib. Comput. 50 1-2 1998 104 122
    • (1998) J. Parallel Distrib. Comput. , vol.50 , Issue.1-2 , pp. 104-122
    • Plimpton, S.1    Attaway, S.2    Hendrickson, B.3    Swegle, J.4    Vaughan, C.5    Gardner, D.6
  • 47
    • 0000042162 scopus 로고    scopus 로고
    • A new parallel method for molecular dynamics simulation of macromolecular systems
    • S. Plimpton, and B. Hendrickson A new parallel method for molecular dynamics simulation of macromolecular systems J. Comp. Chem. 17 3 1996 326
    • (1996) J. Comp. Chem. , vol.17 , Issue.3 , pp. 326
    • Plimpton, S.1    Hendrickson, B.2
  • 48
    • 0037447809 scopus 로고    scopus 로고
    • A load-balancing algorithm for a parallel electromagnetic particle-in-cell code
    • S.J. Plimpton, D.B. Seidel, M.F. Pasik, R.S. Coats, and G.R. Montry A load-balancing algorithm for a parallel electromagnetic particle-in-cell code Comput. Phys. Commun. 152 2 2003 227 241
    • (2003) Comput. Phys. Commun. , vol.152 , Issue.2 , pp. 227-241
    • Plimpton, S.J.1    Seidel, D.B.2    Pasik, M.F.3    Coats, R.S.4    Montry, G.R.5
  • 49
    • 0030172529 scopus 로고    scopus 로고
    • Comments on PPPM, FMM, and the Ewald method for large periodic Coulombic systems
    • E.L. Pollock, and J. Glosli Comments on PPPM, FMM, and the Ewald method for large periodic Coulombic systems Comput. Phys. Commun. 95 1996 93 110
    • (1996) Comput. Phys. Commun. , vol.95 , pp. 93-110
    • Pollock, E.L.1    Glosli, J.2
  • 50
    • 0041887755 scopus 로고    scopus 로고
    • A portable distributed implementation of the parallel multipole tree algorithm
    • [Duke University Technical Report 95-002]
    • W. Rankin, J. Board, A portable distributed implementation of the parallel multipole tree algorithm, IEEE Symposium on High Performance Distributed Computing [Duke University Technical Report 95-002].
    • IEEE Symposium on High Performance Distributed Computing
    • Rankin, W.1    Board, J.2
  • 51
    • 0035870662 scopus 로고    scopus 로고
    • Multigrid methods for classical molecular dynamics simulations of biomolecules
    • C. Sagui, and T. Darden Multigrid methods for classical molecular dynamics simulations of biomolecules J. Chem. Phys. 114 15 2001 6578 6591
    • (2001) J. Chem. Phys. , vol.114 , Issue.15 , pp. 6578-6591
    • Sagui, C.1    Darden, T.2
  • 52
    • 0033024177 scopus 로고    scopus 로고
    • Molecular dynamics simulations of biomolecules: Long-range electrostatic effects
    • C. Sagui, and T.A. Darden Molecular dynamics simulations of biomolecules: Long-range electrostatic effects Ann. Rev. Biophys. Biomol. Struct. 28 1999 155 179
    • (1999) Ann. Rev. Biophys. Biomol. Struct. , vol.28 , pp. 155-179
    • Sagui, C.1    Darden, T.A.2
  • 53
    • 0035339718 scopus 로고    scopus 로고
    • Multiscale fast summation of long-range charge and dipolar interactions
    • B. Sandak Multiscale fast summation of long-range charge and dipolar interactions J. Comp. Chem. 22 7 2001 717 731
    • (2001) J. Comp. Chem. , vol.22 , Issue.7 , pp. 717-731
    • Sandak, B.1
  • 54
    • 0043005053 scopus 로고
    • Load balancing and data locality in adaptive hierarchical N-body method - Barnes-hut, fast multipole and radiosity
    • J.P. Singh, C. Holta, T. Totsuka, A. Gupta, and J. Hennessy Load balancing and data locality in adaptive hierarchical N -body method - Barnes-Hut, Fast Multipole and Radiosity J. Parallel Distrib. Comput. 27 2 1995 118 141
    • (1995) J. Parallel Distrib. Comput. , vol.27 , Issue.2 , pp. 118-141
    • Singh, J.P.1    Holta, C.2    Totsuka, T.3    Gupta, A.4    Hennessy, J.5
  • 55
    • 0037197257 scopus 로고    scopus 로고
    • Multiple grid methods for classical molecular dynamics
    • R.D. Skeel, I. Tezcan, and D.J. Hardy Multiple grid methods for classical molecular dynamics J. Comp. Chem. 23 6 2002 673 684
    • (2002) J. Comp. Chem. , vol.23 , Issue.6 , pp. 673-684
    • Skeel, R.D.1    Tezcan, I.2    Hardy, D.J.3
  • 56
    • 0034506266 scopus 로고    scopus 로고
    • Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions
    • A. Toukmaji, C. Sagui, J. Board, and T. Darden Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions J. Chem. Phys. 113 24 2000 10913 10927
    • (2000) J. Chem. Phys. , vol.113 , Issue.24 , pp. 10913-10927
    • Toukmaji, A.1    Sagui, C.2    Board, J.3    Darden, T.4
  • 57
    • 0030163950 scopus 로고    scopus 로고
    • Ewald summation techniques in perspective: A survey
    • A.Y. Toukmaji, and J.A. Board Ewald summation techniques in perspective: a survey Comput. Phys. Commun. 95 1996 73 92
    • (1996) Comput. Phys. Commun. , vol.95 , pp. 73-92
    • Toukmaji, A.Y.1    Board, J.A.2
  • 58
    • 0025202156 scopus 로고
    • Structure of apolipoprotein A-I in three homogeneous reconstituted high density lipoprotein particles
    • J.H. Wald, E.S. Krul, and A. Jonas Structure of apolipoprotein A-I in three homogeneous reconstituted high density lipoprotein particles J. Biol. Chem. 265 1990 20037 20043
    • (1990) J. Biol. Chem. , vol.265 , pp. 20037-20043
    • Wald, J.H.1    Krul, E.S.2    Jonas, A.3
  • 59
    • 84967045101 scopus 로고
    • Astrophysical N -body simulations using hierarchical tree data structures
    • IEEE Computer Society Press Silver Spring, MD
    • M.S. Warren, and J.K. Salmon Astrophysical N -body simulations using hierarchical tree data structures Supercomputing '92 1992 IEEE Computer Society Press Silver Spring, MD 570 576
    • (1992) Supercomputing '92 , pp. 570-576
    • Warren, M.S.1    Salmon, J.K.2
  • 60
    • 1842471081 scopus 로고
    • A portable parallel particle program
    • M.S. Warren, and J.K. Salmon A portable parallel particle program Comput. Phys. Commun. 87 1-2 1995 266 290
    • (1995) Comput. Phys. Commun. , vol.87 , Issue.1-2 , pp. 266-290
    • Warren, M.S.1    Salmon, J.K.2
  • 61
    • 0347768279 scopus 로고    scopus 로고
    • Compression of particle data from hierarchical approximate methods
    • D.Y. Yang, A. Grama, V. Sarin, and K. Ramakrishnan Compression of particle data from hierarchical approximate methods ACM Trans. Math. Software 27 3 2001 317 339
    • (2001) ACM Trans. Math. Software , vol.27 , Issue.3 , pp. 317-339
    • Yang, D.Y.1    Grama, A.2    Sarin, V.3    Ramakrishnan, K.4
  • 62
    • 33744994616 scopus 로고
    • The fast Fourier-Poisson method for calculating Ewald sums
    • D. York, and W.T. Yang The fast Fourier-Poisson method for calculating Ewald sums J. Chem. Phys. 101 1994 3298 3300
    • (1994) J. Chem. Phys. , vol.101 , pp. 3298-3300
    • York, D.1    Yang, W.T.2
  • 63
    • 0004973907 scopus 로고    scopus 로고
    • An adaptive multigrid technique for evaluating long-range forces in biomolecular simulations
    • L.Y. Zaslavsky, and T. Schlick An adaptive multigrid technique for evaluating long-range forces in biomolecular simulations Appl. Math. Comput. 97 1998 237 250
    • (1998) Appl. Math. Comput. , vol.97 , pp. 237-250
    • Zaslavsky, L.Y.1    Schlick, T.2


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