Efficient Parallel Implementation of Molecular Dynamics with Embedded Atom Method on Multi-core Platforms

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Efficient Parallel Implementation of Molecular
Dynamics with Embedded Atom Method on Multi-core
Platforms

• Reporter Jilin Zhang
• AuthorsChangjun Hu, Yali Liu, and Jianjiang Li
• Information Engineering School, University of
  Science and Technology Beijing, Beijing, P.R.China

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Outline

• 1 Motivation
• 2 Related Works
• 3 Spatial Decomposition Coloring (SDC) Approach
• 4 Short-Range Forces Calculations of EAM using
  SDC method
• 5 Experiments and Discussion
• 6 Conclusion and Future Directions

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1 Motivation

• The process of molecular dynamics simulations

set init_state
Fig. 1 the process of molecular dynamics
simulations.
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1 Motivation

• the intensive computation appears in short-range
  force calculations procedure of MD simulations
• Neighbor-list method decreases the intensive
  computation largely. It make each atom only
  interacts with atoms in its neighbor region.
• Newtons third law can have the force
  computations. And it brings the reduction
  operations on irregular arrays

Fig. 2 codes of force caluclations.
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2 Related Works --- parallel reduction
operations on irregular arrays

• Some types of solutions
• enclosing reduction operation in a critical
  section
• privating the reduction array
• using redundant computations strategy

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2 Related Works --- parallel reduction
operations on irregular arrays

• enclosing reduction operation in a critical
  section
• create a critical section in inner loop
• straight and easy to implement parallelization.
• high synchronization cost arose by critical
  region, atomic or lock involved in inner loop

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2 Related Works --- parallel reduction
operations on irregular arrays

• private the reduction array
• each thread have to update share array in
  critical region according the value of its
  private array
• it reduce times of entering into critical region
  and reduce synchronization cost.
• high memory overhead of private array
• limit number of particles allowed in simulations
• compete for cache space and decrease program
  speed

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2 Related Works --- parallel reduction
operations on irregular arrays

• redundant computations strategy
• does not use Newtons third law. So each pair
  interaction has to be calculated twice.
• the high parallelizability since data dependence
  has been removed between the loop iterations
• there are double computations and that neighbor
  list requires more memory space.

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3 Spatial Decomposition Coloring (SDC) Approach

• Spatial Decomposition (SD) method
• distributed memory multi-processors involving
  several hundreds of processors
• change all array declarations and all loop
  bounds, and explicitly codes the periodic
  transfer of the boundary data between processors.
  
• It is simple to implement SD in OpenMP.

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3 Spatial Decomposition Coloring (SDC) Approach

• SD method places a restriction on parallelism in
  OpenMP.
• synchronization will be required to ensure that
  multiple threads do not attempt to update the
  same atom simultaneously.

Fig. 3 SD method.
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3 Spatial Decomposition Coloring (SDC) Approach

• SDC method
• SDC method consists of the following steps
• Step 1) Split domain
• Step 2) Coloring subdomains
• Step 3) Parallel Computing

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3 Spatial Decomposition Coloring (SDC) Approach

• SDC method
• SDC method consists of the following steps
• Step 1) Split domain
• Split the spatial domain into subdomains.
• Length of a subdomain must be longer than
  diameter.
• Number of subdomains in dimension decomposed
  should be even.

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3 Spatial Decomposition Coloring (SDC) Approach

• SDC method
• SDC method consists of the following steps
• Step 2) Coloring subdomains
• The number of subdomains with each color must be
  equal
• each subdomain is surrounded only by those
  subdomains with different colors.

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3 Spatial Decomposition Coloring (SDC) Approach

• SDC method
• SDC method consists of the following steps
• Step 3) Parallel Computing
• Calculations of forces on subdomains with one
  color can be run in parallel.
• a barrier should be given for waiting all threads
  to complete computation on this color.
• Calculations on subdomains with different colors
  must run in a serial fashion.

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3 Spatial Decomposition Coloring (SDC) Approach

• SDC method
• advantage
• neighbor list usually doesnt be updated in every
  time-step ?Cost of SDC method is very lowest.
• higher-dimensional decomposition method creates
  more subdomains. ?scalable and suitable on
  multi-core and many-core architectures.
• disadvantage
• Spatial Decomposition method ?Overload imbalance
• ? under condition of simulation system has
  uniformity of density

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4 Short-Range Forces Calculations of EAM using
SDC method

• EAM method
• short-range forces
• the intensive computation
• three computational phases
• the most time consuming parts are 1 and 3

Fig. 4 short-range forces in EAM method.
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4 Short-Range Forces Calculations of EAM using
SDC method

• The parallel procedure of short-range forces
  calculations using SDC method
• 1) Run electron density computations using SDC
  method
• 2) Calculate embedding function value and their
  derivative in parallel
• 3) Run force calculations using SDC method

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4 Short-Range Forces Calculations of EAM using
SDC method

• force calculations based on SDC method
• L1 computations on subdomains with different
  color
• L2 computations on subdomains with same color
• L3 deals with all atoms that constitute a
  subdomain
• L4 deals with neighbors of a atom

Fig. 5 forces calculations using SDC.
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5 Experiments and Discussion

• Experimental environment
• Four Intel Xeon(R) Quad-core E7320 (L2 Cache 4MB)
  processors, 16 GB memory
• OS is Fedora release 9 with kernel 2.6.25. The
  compiler is gcc 4.3.0.
• Experimental cases
• observe micro-deformation behaviors of pure Fe
  metals material
• ---came from XMD program
• under periodic boundary conditions
• initial state -- body-centered cubic (bcc)
  lattice arrangement
• test cases
• Small-scale case (1) 54,000 atoms
• Medium-scale case (2) 265,302 atoms
• Large-scale case (3) 1,062,882 atoms
• Large-scale case (4) 3,456,000 atoms

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Table 1. The Speedups of Spatial Decomposition
Coloring (SDC) Methods
Speedup Small case (1) on 216 cores Small case (1) on 216 cores Small case (1) on 216 cores Small case (1) on 216 cores Small case (1) on 216 cores Small case (1) on 216 cores Medium case (2) on 216 cores Medium case (2) on 216 cores Medium case (2) on 216 cores Medium case (2) on 216 cores Medium case (2) on 216 cores Medium case (2) on 216 cores
Speedup 2 3 4 8 12 16 2 3 4 8 12 16
SDC (one-dim) 1.71 2.46 3.07 4.17 1.84 2.64 3.37 6.24 6.33
SDC (two-dim) 1.70 2.46 3.07 4.74 5.90 6.43 1.84 2.65 3.39 6.20 8.89 10.90
SDC (three-dim) 1.66 2.40 2.99 4.61 5.74 6.30 1.82 2.65 3.36 6.16 8.76 10.78
Large case (3) on 216 cores Large case (3) on 216 cores Large case (3) on 216 cores Large case (3) on 216 cores Large case (3) on 216 cores Large case (3) on 216 cores Large case (4) on 216 cores Large case (4) on 216 cores Large case (4) on 216 cores Large case (4) on 216 cores Large case (4) on 216 cores Large case (4) on 216 cores
2 3 4 8 12 16 2 3 4 8 12 16
SDC (one-dim) 1.86 2.76 3.67 6.82 9.76 9.59 1.88 2.79 3.66 6.30 9.97 9.82
SDC (two-dim) 1.87 2.78 3.64 6.74 9.73 12.31 1.87 2.80 3.65 6.77 9.84 12.42
SDC (three-dim) 1.86 2.75 3.64 6.64 9.65 12.29 1.87 2.80 3.67 6.74 9.82 12.34
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5 Experiments and Discussion

• the scalability of our SDC method. performance of
  multi-dimensional SDC method has been improved
  with the increase in the number of cores and the
  increase in the number of atoms.
• performance of SDC methods. We can see that
  two-dimensional SDC method achieves highest
  efficiency.
• two-dimensional decomposition algorithm strives
  to make subdomains with small surface area and
  large volume, which results in better cache
  locality compared to the one-dimensional
  decomposition strategy.
• three-dimensional SDC method slightly degrades
  the performance due to the more overhead of
  fork-join threads and scheduling.

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Fig. 6 The speedup of two-dimensional Spatial
Decomposition Coloring (SDC) method, Critical
Section (CS) method, Share Array Privatization
(SAP) method and Redundant Computations (RC)
method.
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5 Experiments and Discussion

• SDC method achieves a nearly linear speedup and
  highest speedup than other methods
• The reason of nearly linear speedup is that the
  low synchronization cost of implicit barriers in
  our method can be amortized over a large amount
  of computation.
• CSmethod
• achieves lowest efficiency. CS method encloses
  reduction operations on irregular array in
  critical section.
• SAPmethod
• performance degrade with the increase of the
  number of executing cores. memory
  overheadsynchronization overhead
• RC VS SDC
• there is nearly two-fold computation work for the
  short-range force calculations in RC method than
  in SDC method, the efficiency of RC method is low
  than that of SDC method.

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Conclusion and Future Directions

• A scalable spatial decomposition coloring (SDC)
  method
• To solve a class of short-range force
  calculations problems on shared memory multi-core
  platforms
• It is scalable not only to large simulation
  system but also to many-core architectures
• Future directions
• To study SDC method on NUMA memory architecture
• To implement SDC method using MPIOpenMP in
  multi-core cluster

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• Thank You !