Benchmarking Results, PMEMD 9

Compiled below are benchmarks for a range of hardware and a range of problems, something like 38 benchmarks in total. We cover here a wide range of systems using from 1 up to 320 cpu's, and we cover pme problems with sizes ranging from ~23k to ~193k atoms and one medium generalized Born benchmark. Both the systems and problems overlap somewhat with benchmarks run by Ross Walker at SDSC (thanks Ross!), but there are enough differences that both sets should be considered.

All these benchmarks were run using formatted output for trajectories (ioutfm = 0). There is a new binary trajectory format based on netCDF that works very well in most instances that can improve very high end scaling by as much as 5-10%, and it is worth a try if you do very high cpu count runs.

Bob Duke
NIEHS and UNC-Chapel Hill
May 19, 2006

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BENCHMARK DESCRIPTIONS

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HFVa - NVT ensemble, PME, 193,013 atoms

Human Factor Va (blood coagulation cascade) protein in TIP3P water.
Benchmark contributed by Dr. Chang Jun Lee of Prof. Lee Pedersen's lab.
This benchmark is not yet available for general public use.
Orthogonal periodic unit cell, 105.28 x 148.49 x 125.35 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 9.0 angstrom, reciprocal space FFT grid dimensions 108 x 150 x 128.
2 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 100 steps (mdout).
Trajectory printed every 250 steps (mdcrd).
Equilibration temperature = 300K.

HFVa - NPT ensemble, PME, 193,013 atoms

Human Factor Va (blood coagulation cascade) protein in TIP3P water.
Benchmark contributed by Dr. Chang Jun Lee of Prof. Lee Pedersen's lab.
This benchmark is not yet available for general public use.
Orthogonal periodic unit cell, 105.28 x 148.49 x 125.35 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 9.0 angstrom, reciprocal space FFT grid dimensions 108 x 150 x 128.
2 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 100 steps (mdout).
Trajectory printed every 250 steps (mdcrd).
Equilibration temperature = 300K.

FACTOR IX - NVT ensemble, PME, 90,906 atoms

Human Factor IX (blood coagulation cascade) protein in TIP3P water.
Benchmark contributed by Dr. Lalith Perera of Prof. Lee Pedersen's lab.
Orthogonal periodic unit cell, 142.09 x 83.34 x 78.68 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 8.0 angstrom, reciprocal space FFT grid dimensions 144 x 90 x 80.
1.5 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 50 steps (mdout).
Trajectory printed every 250 steps (mdcrd).
Equilibration temperature = 300K.

This benchmark of Factor IX differs from the default Amber Factor IX benchmark in that it uses the NVT (vs. NVE) ensemble (ie., there is a thermostat), it outputs energies more frequently, and it outputs a trajectory at a frequency that is more than adequate to meet most needs (general consensus seems to be that a trajectory snapshop every picosecond is generally more than sufficient). There is slight additional overhead associated with the NVT ensemble compared to the NVE ensemble. Also, printing a trajectory at high frequency tests the file i/o capability of both the hardware and software.

FACTOR IX - NPT ensemble, PME, 90,906 atoms

Human Factor IX (blood coagulation cascade) protein in TIP3P water.
Benchmark contributed by Dr. Lalith Perera of Prof. Lee Pedersen's lab.
Orthogonal periodic unit cell, 142.09 x 83.34 x 78.68 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 8.0 angstrom, reciprocal space FFT grid dimensions 144 x 90 x 80.
1.5 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 50 steps (mdout).
Trajectory printed every 250 steps (mdcrd).
Equilibration temperature = 300K.

This benchmark of Factor IX differs from the default Amber Factor IX benchmark in that it uses the NPT (vs. NVE) ensemble (ie., there is a thermostat and barostat), it outputs energies more frequently, and it outputs a trajectory at a frequency that is more than adequate to meet most needs (general consensus seems to be that a trajectory snapshop every picosecond is generally more than sufficient). The NPT ensemble offers additional challenges to scaling over both the NVE and NVT ensemble. Also, printing a trajectory at high frequency tests the file i/o capability of both the hardware and software.

FACTOR IX - NVE ensemble, PME, 90,906 atoms

Human Factor IX (blood coagulation cascade) protein in TIP3P water.
This is the Amber Factor IX benchmark and is run exactly as distributed in the Amber 9 benchmarks tree aside from total dynamics step count.
Benchmark contributed by Dr. Lalith Perera of Prof. Lee Pedersen's lab.
Orthogonal periodic unit cell, 142.09 x 83.34 x 78.68 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 8.0 angstrom, reciprocal space FFT grid dimensions 144 x 90 x 80.
1.5 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 100 steps (mdout).
Trajectory NOT printed.
Equilibration temperature = 300K.

JAC - NVE ensemble, PME, 23,558 atoms

Dihydrofolate Reductase (DHFR) protein in TIP3P water.
This is the Joint Amber-Charmm Benchmark, and is run exactly as distributed in the Amber 9 benchmarks tree aside from total dynamics step count.
Orthogonal periodic unit cell, 62.23 x 62.24 x 62.23 angstrom.
Full Particle Mesh Ewald simulation, direct nonbonded cutoff 9.0 angstrom, reciprocal space FFT grid dimensions 64 x 64 x 64.
1.0 femtosecond timestep, bonds to H constrained (SHAKE).
Energies printed every 100 steps (mdout).
Trajectory NOT printed.
Equilibration temperature = 300K.

MB - Generalized Born, 2492 atoms

Myoglobin protein, implicit solvent.
This is the Amber generalized Born myoglobin benchmark and is run exactly as distributed in the Amber 9 benchmarks tree aside from total dynamics step count.
Generalized Born simulation (igb=1), nonbonded cutoff 20.0 angstrom.
1.0 femtosecond timestep, bonds to H constrained (SHAKE).
Slowly varying forces evaluation every 4 steps (nrespa=4).
Energies printed every 200 steps (mdout).
Trajectory NOT printed.

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MACHINE DESCRIPTIONS

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IBM SP5

IBM p575 Power 5, bassi.nersc.gov, 118 8-cpu nodes
1.9 GHz Power 5+ cpu, 2 MB L2 cache, 36 MB L3 cache, 32 GB memory per node
IBM "Federation" HPS switch (node interconnect)
GPFS file system
IBM XL Fortran, MASSV vector math library

This is an incredibly well tuned sp5, and pmemd scales better here than on other sp5's I have seen. My hat is off to the NERSC folks for how they are getting this machine to perform.

IBM SP4

IBM p655+ Power 4, dslogin.sdsc.edu, 272 8-cpu nodes
1.7 GHz Power 4 cpu, 32 GB memory per node
IBM "Federation" HPS switch (node interconnect)
GPFS file system
IBM XL Fortran, MASSV vector math library

Cray XT3

Cray XT3 MPP, bigben.psc.edu, 2068 1-cpu nodes
2.4 GHz Opteron cpu, 1 GB memory per node
Cray proprietary switch (node interconnect)
Lustre file system

The file system software on this machine can cause stalling of high scaling jobs on disk i/o. Recently Cray has released a buffering library to help alleviate this problem (suggestions for PMEMD configuration and runtime environment variables will be posted soon on the amber web site). This problem is mostly seen when jobs that do huge amounts of file i/o are running concurrently with your job. The benchmark data given below was taken before the machine was overloaded with this type of job. For this machine or any other machine, if the RunMD time in the system logfile for the master process (0) is significantly larger than the time for other processes (say more than about 4-5 times larger) you may be encountering this problem. Using binary trajectory files will not help, but using the Cray iobuf library and ioutfm=0 should at least reduce the impact of this system imbalance. See the amber web site for more details. The Cray XD1 is probably subject to similar problems.

SGI Altix

SGI Altix 3700 Bx2, cobalt.ncsa.uiuc.edu 2 512-cpu nodes
1.6 GHz Itanium 2 cpu, 9 MB L3 cache, 1024 GB memory per node
SGI NUMAlink 4 node interconnect
File system details unknown

Opteron Infiniband Cluster

Linux Opteron cluster, jacquard.nersc.gov, 356 2-cpu nodes
2.2 GHz Opteron cpu, 6 GB memory per node
Mellanox Infiniband node interconnect / MVAPICH
GPFS file system
Pathscale Fortran 90 compiler, math library not used

Dell/Intel Infiniband Cluster

Dell Linux Xeon cluster, topsail.unc.edu , 512 2-cpu nodes
3.6 GHz Xeon (EM64T) cpu, 2 MB L2 cache, 4 GB memory per node
Infiniband node interconnect / MVAPICH
IBRIX Parallel Files System
Intel Fortran 90 compiler, Intel MKL

HP Alphaserver / Quadrics Cluster

HP Alphaserver ES45, lemieux.psc.edu, 750 4-cpu nodes
1 GHz Alpha EV6.8CB cpu, 4 GB memory per node
Quadrics switch (node interconnect)
There are both local file systems on the nodes and a shared scratch file system. Access to the scratch file system is prone to stalling jobs, so I would recommend working out how to use the $LOCAL file system (which I have NOT done myself; I typically just benchmark to $HOME, but there is limited storage there). See the PSC lemieux user manual online (www.psc.edu).

NOTE - You should run using the "2-rail" option for the interconnect when using 64 or more cpu's (at 32 it may also help, depending on problem size). See the PSC lemieux user manual online (www.psc.edu).

IBM BG/L

IBM BlueGene, IBM Rochester BlueGene Capacity on Demand Center, 1024 2-cpu nodes
700 MHz PowerPC 440 cpu, 4 MB L3 cache, 0.5 GB memory per node
IBM proprietary switch (node interconnect)
GPFS file system
IBM XL Fortran, MASSV vector math library

The machine was used with the processors in "virtual-node" mode instead of "coprocessor" mode (performance was significantly better). Code was compiled with -qarch=440 instead of -qarch=440d (ie., special math instructions not used, performance was better). Code was compiled without -qhot (using this causes incorrect results). The interconnect for BG/L is configurable; we used a partition with an 8 x 8 x 8 geometry for all benchmarks.

The MASSV library significantly improves generalized Born performance, but at the time of the tests could not be used for really large simulations due to a bug in the library. It worked fine for the MB benchmark (2492 atoms).

The IBM BG/L architecture is unique in that a less powerful cpu without much memory was intentionally used with a very high performance configurable cpu interconnect. To take full advantage of this architecture, features must be added to PMEMD; this work is anticipated to be completed for PMEMD 10.

SGI Origin 3800

SGI Origin 3800, zephyr.isis.unc.edu 1 64-cpu node
0.5 GHz MIPS R14000 cpu, 8 MB L2 cache, 64 GB memory per node
Symmetric multiprocessor, memory-interconnected
File system details unknown

Intel Xeon gigabit ethernet cluster

Duke's workstation cluster (tiger, lion), 2 2-cpu nodes
3.2 GHz Intel Xeon cpu, 0.5 MB cache, 2 GB memory per node
Gigabit ethernet, dedicated Intel server NIC's, dedicated crossover (XO) cable (no switch needed) / MPICH-1.2.6
Intel Fortran 90 compiler, Intel MKL

Dell EM64T Pentium dual cpu

Duke's standalone workstation (cheetah), 1 2-cpu node
3.0 GHz Intel Pentium D cpu (EM64T), 1 MB cache, 2 GB memory per node
Shared memory interconnect / MPICH-1.2.6 Intel Fortran 90 compiler, Intel MKL

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BENCHMARK RESULTS

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IBM SP5 - HFVa - NVT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.112          100
    4          0.220           98
    8          0.427           95
   16          0.824           92
   32          1.58            88
   64          2.98            83
   96          4.15            77
  128          5.24            73
  160          6.17            69
  192          7.02            65
  224          7.78            62
  256          8.07            56
  288          8.55            53
  320          9.0             50

*******************************************************************************

IBM SP5 - HFVa - NPT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.112          100
    4          0.218           96
    8          0.422           93
   16          0.816           89
   32          1.55            85
   64          2.94            81
   96          4.09            75
  128          5.14            72
  160          6.00            67
  192          6.80            63
  224          7.02            56
  256          7.58            53
  288          7.71            48
  320          8.0             45

*******************************************************************************

IBM SP5 - FACTOR IX - NVE ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.245          100
    4          0.476           97
    8          0.946           96
   16          1.80            92
   32          3.28            84
   64          6.17            79
   96          8.58            73
  128         10.45            67
  160         11.78            60
  192         13.22            56
  224         13.79            50
  256         14.6             47
  288         15.4             44
  320         15.4             44

*******************************************************************************

IBM SP5 - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.243          100
    4          0.475           98
    8          0.931           96
   16          1.78            92
   32          3.26            84
   64          6.06            78
   96          8.15            70
  128          9.74            63
  160         10.08            46
  192         11.08            47
  224         11.78            43
  256         12.23            39
  288         12.58            36
  320         13.5             35

*******************************************************************************

IBM SP5 - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.506          100
    4          0.995           98
    8          1.95            96
   16          3.69            91
   32          7.08            87
   64         12.52            77
   96         16.62            68
  128         18.78            58
  160         20.1             50
  192         19.2             40
  224         22.2             39
  256         22.2             34

*******************************************************************************

IBM SP5 - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.511          100
    4          1.016          100
    8          2.02            99
   16          3.93            96
   32          7.32            90
   64         12.71            78
  128         19.63            60

*******************************************************************************

IBM SP4 - FACTOR IX - NVE ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.245          100
    4          0.476           97
    8          0.946           96
   16          1.80            92
   32          3.28            84
   64          6.17            79
   96          8.58            73
  128         10.45            67
  160         11.78            60
  192         13.22            56
  224         13.79            50
  256         14.6             47
  288         15.4             44
  320         15.4             44

*******************************************************************************

IBM SP4 - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.208          100
    4          0.385           93
    8          0.689           83 
   16          1.301           78 
   32          2.409           72
   64          4.334           65 
   96          5.972           60
  128          7.082           53
  192          8.698           44
  256          8.471           32 

*******************************************************************************

IBM SP5 - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.506          100
    4          0.995           98
    8          1.95            96
   16          3.69            91
   32          7.08            87
   64         12.52            77
   96         16.62            68
  128         18.78            58
  160         20.1             50
  192         19.2             40
  224         22.2             39
  256         22.2             34

*******************************************************************************

Cray XT3 - HFVa - NVT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.098          100
    4          0.184           94
    8          0.365           93
   16          0.711           91
   32          1.34            85
   64          2.49            79
   96          3.08            65
  128          4.24            67
  160          4.94            63
  192          5.38            57
  224          5.88            53
  256          5.57            44
  288          5.86            41
  320          6.15            39

*******************************************************************************

Cray XT3 - HFVa - NPT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.085          100
    4          0.171          101
    8          0.343          101
   16          0.649           96
   32          1.26            93
   64          2.30            85
   96          3.15            77
  128          3.98            73
  160          4.58            68
  192          4.91            60
  224          5.37            57
  256          5.10            47
  288          5.28            43
  320          5.57            41

*******************************************************************************

Cray XT3 - FACTOR IX - NVT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.217          100
    4          0.398           92
    8          0.820           94
   16          1.57            90
   32          2.83            82
   64          4.93            71
   96          6.89            66
  128          7.85            57
  160          8.70            50
  192          9.39            45
  224         10.05            41
  256         10.20            37
  288         10.29            33
  320         10.05            29

*******************************************************************************

Cray XT3 - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.218          100
    4          0.400           92
    8          0.795           91
   16          1.56            89
   32          2.80            80
   64          4.70            67
   96          6.23            59
  128          7.69            55
  160          7.67            44
  192          8.53            41
  224          9.00            37
  256          9.60            34
  288          9.74            31
  320          9.89            28

*******************************************************************************

Cray XT3 - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.482          100
    4          0.904           94
    8          1.80            93
   16          3.46            90
   32          6.26            81
   64         10.54            68
   96         13.09            57
  128         15.7             51
  160         14.9             39
  192         16.0             35
  224         15.7             29

*******************************************************************************

Cray XT3 - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.435          100
    4          0.867          100
    8          1.71            99
   16          3.35            96
   32          6.45            93
   64         11.37            82
  128         18.78            67

*******************************************************************************

SGI Altix - FACTOR IX - NVT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.311          100
    4          0.592           95
    8          1.17            94
   16          2.10            85
   32          3.54            71
   64          6.29            63
   96          7.71            52
  128          6.17            31

*******************************************************************************

SGI Altix - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.293          100
    4          0.586          100
    8          1.14            97
   16          2.03            87
   32          3.41            73
   64          5.94            64
   96          7.28            52
  128          6.00            32

*******************************************************************************

SGI Altix - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.738          100
    4          1.38            94
    8          2.86            97
   16          5.30            90
   32          9.19            78
   64         12.17            51
   96         15.16            43
  128         11.84            25

*******************************************************************************

SGI Altix - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.385          100
    4          0.762           99
    8          1.35            87
   16          2.88            93
   32          4.91            80
   64          7.71            63
  128          7.71            31

*******************************************************************************

Opteron Infiniband Cluster - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.226          100
    4          0.438           97
    8          0.842           93
   16          1.58            87
   32          2.77            76
   64          4.91            68
   96          6.35            58
  128          7.04            49
  160          7.20            40

*******************************************************************************

Opteron Infiniband Cluster - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.491          100
    4          0.947           96
    8          1.82            92
   16          3.22            82
   32          6.08            77
   64         10.05            64
   96         11.84            50
  128         12.00            38

*******************************************************************************

Opteron Infiniband Cluster - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.426          100
    4          0.842           99
    8          1.66            97
   16          3.25            95
   32          6.00            88
   64         10.80            79
   96         14.40            70

*******************************************************************************

Dell/Intel Infiniband Cluster - HFVa - NVT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.101          100
    4          0.190           94
    8          0.355           87
   16          0.690           85
   32          1.25            77
   64          2.30            71
   96          3.10            64
  128          3.62            56
  160          4.15            51
  192          4.45            46
  224          4.50            40

*******************************************************************************

Dell/Intel Infiniband Cluster - HFVa - NPT ensemble, PME, 193,013 atoms

#procs         nsec/day       scaling, %

    2          0.101          100
    4          0.188           93
    8          0.356           88
   16          0.653           81
   32          1.22            76
   64          2.25            70
   96          3.02            63
  128          3.63            56
  160          3.98            49
  192          4.13            43
  224          4.06            36

*******************************************************************************

Dell/Intel Infiniband Cluster - FACTOR IX - NVT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.217          100
    4          0.393           92
    8          0.778           88
   16          1.48            86
   32          2.59            76
   64          4.66            67
   96          5.94            57
  128          6.48            47
  160          6.89            40

*******************************************************************************

Dell/Intel Infiniband Cluster - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.211          100
    4          0.393           93
    8          0.741           88
   16          1.45            86
   32          2.54            75
   64          4.47            66
   96          5.63            56
  128          6.42            47
  160          6.65            39

*******************************************************************************

Dell/Intel Infiniband Cluster - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.470          100
    4          0.895           95
    8          1.71            91
   16          3.03            81
   32          5.84            78
   64          9.60            64
   96         11.1             49

*******************************************************************************

Dell/Intel Infiniband Cluster - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.584          100
    4          1.15            99
    8          2.22            95
   16          4.15            89
   32          6.86            73
   64         10.7             57
   96         10.8             39

*******************************************************************************

HP Alphaserver/Quadrics Cluster - FACTOR IX - NVT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.132          100
    4          0.254           96
    8          0.455           86
   16          0.825           78
   32          1.36            65
   64          2.74            65 *
   96          3.37            53 *
  128          3.65            43 *
  160          4.47            42 *

  * - 2-rail option used on interconnect

*******************************************************************************

HP Alphaserver/Quadrics Cluster - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.130          100
    4          0.246           94
    8          0.445           85
   16          0.790           76
   32          1.34            64
   64          2.66            64 *
   96          3.43            55 *
  128          3.37            40 *
  160          4.02            39 *

  * - 2-rail option used on interconnect

*******************************************************************************

HP Alphaserver/Quadrics Cluster - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.282          100
    4          0.540           96
    8          0.982           87
   16          1.69            75
   32          3.20            71
   64          5.61            62 *
   80          6.52            58 *
   96          4.49            33 *

  * - 2-rail option used on interconnect

*******************************************************************************

IBM BG/L - FACTOR IX - NVE ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.054          100
    4          0.103           96
    8          0.200           93
   16          0.388           90
   32          0.721           84
   64          1.33            78
   96          1.92            74
  128          2.42            70
  160          2.84            66
  192          3.29            64
  224          3.43            57
  256          3.77            55
  288          4.00            52
  320          4.00            47
  352          4.18            44
  384          4.10            40
  416          4.21            38
  448          4.15            35

*******************************************************************************

IBM BG/L - FACTOR IX - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.109          100
    4          0.211           97
    8          0.408           94
   16          0.758           87
   32          1.49            86
   64          2.84            82
   96          3.89            75
  128          4.85            70
  160          5.54            64
  192          5.68            54
  224          6.08            50
  256          6.35            46
  288          6.55            42
  320          6.35            36

*******************************************************************************

IBM BG/L - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    2          0.099          100
    4          0.196           99
    8          0.391           99
   16          0.771           98
   32          1.50            95
   64          2.84            90
   96          3.89            82
  112          4.32            78
  128          5.14            81
  144          5.33            75

*******************************************************************************

SGI Origin 3800 - FACTOR IX - NVT ensemble, PME, 90,906 atoms

#procs         nsec/day       scaling, %

    2          0.074          100
    4          0.143           97
    8          0.284           96
   12          0.410           93
   16          0.527           89

*******************************************************************************

SGI Origin 3800 - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    2          0.166          100
    4          0.320           96
    8          0.640           96
   12          0.909           91
   16          1.200           90

*******************************************************************************

Intel Xeon gigabit ethernet cluster - FACTOR IX - NPT ensemble, PME,
90,906 atoms

#procs         nsec/day       scaling, %

    1          0.116           --
    2          0.182          100
    4          0.293           80

*******************************************************************************

Intel Xeon gigabit ethernet cluster - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day       scaling, %

    1          0.254           --
    2          0.432          100
    4          0.702           81

*******************************************************************************

Intel Xeon gigabit ethernet cluster - MB - Generalized Born, 2492 atoms

#procs         nsec/day       scaling, %

    1          0.292           --
    2          0.554          100
    4          1.094           99

*******************************************************************************

Dell EM64T Pentium dual cpu - FACTOR IX - NPT ensemble, PME, 90,906 atoms

#procs         nsec/day

    1          0.108
    2          0.189

*******************************************************************************

Dell EM64T Pentium dual cpu - JAC - NVE ensemble, PME, 23,558 atoms

#procs         nsec/day

    1          0.300
    2          0.520

*******************************************************************************