Statistical Thermostats

7/27/2019 Statistical Thermostats

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MitgliedderHelmholtz-Gemeinschaft

Efficient CommunicationSchemes for Stochastic

Thermostats in parallelMD Simulations

September 25, 2012 Felix Uhl


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Parallel Stochastic ThermostatsOutline

A Short Introduction to Molecular Dynamics

Thermostats

Why Thermostats?The Andersen ThermostatThe Lowe-Andersen Thermostat

Implementation of the Lowe-Andersen Thermostat

The IBIsCO code

The Current Lowe-Andersen ImplementationThe New Implementation of the Lowe-Andersen ThermostatMore Ways to Parallelize the Lowe-Andersen Thermostat

September 25, 2012 Felix Uhl Slide 2


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Parallel StochasticThermostatsPart I: A Short Introduction to MolecularDynamics



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A Short Introduction to Molecular DynamicsBasic Theory

System of point like particles

Coordinates: {r(t)}, momenta:p(t)

Newtons equations of motion:

md2ridt2

= i

iV(r)

Etot = Ekin + V, Ekin,i =p2i

2mi=

1

2miv

2i , V = V(r)



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A Short Introduction to Molecular DynamicsNumerical Solution of Hamiltons Equations of Motion

Solving equations of motion numerically via discretization

Starting positions and velocities are given at time t= 0

1 r(t+ t) = r(t) + v(t)t+ 12mF(t)t2

2 F(t+ t) = V(r(t+ t))

3 v(t+ t) = v(t) + 12m [F(t) + F(t+ t)] t

4 If t< tmax then repeat



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Parallel StochasticThermostatsPart II: Thermostats



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ThermostatsWhy Thermostats?

TD: Ekin =3

2KBT

CM:Ekin =

1

N

N

i=1

1

2miv2

i

3

2KBT =

1

N

N

i=

1

1

2miv

2i

Boltzmann Distribution

A Boltzmann distribution

corresponds to a specific

temperature 05e-05

0.0001

0.00015

0.0002

0.00025

0 300 600 900 1200 1500 1800

Probability

de

nsity

Speed / (m/s)

Boltzmann distributionHe at 298.15 K



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ThermostatsWhy Thermostats? NVE-Simulation

Give particles velocities according to Boltzmann

distribution

Guess starting positions



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distribution


2

4

6

0 100 200 300 400

Temperature

Timesteps

Evolution of Temperature



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distribution


2

4

6

0 100 200 300 400

Temperature

Timesteps

Evolution of Temperature

1 Optimize geometry with respect to the energy

2 Add/subtract kinetic energy from the system



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ThermostatsThe Andersen Thermostat

0

y

0 x

Simulation Cell with a Real and a Bath System Real system (grey)

Bath system(red)

Bath has fixed temperature

Collisions between realparticles and bath particles

adjust temperature in real

system

Implementation

Randomly select particles up to a certain frequency. The

velocity is replaced by a random velocity according to the

Boltzmann distribution.



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ThermostatsThe Lowe-Andersen Thermostat

1 2

v1

v2



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1 2

v1

v2

v12,proj

1 Project v1 v2 on theconnecting unit vector



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1 2

v1

v2

v12,proj

vnew


2 Pick random new velocity

from Boltzmann

distribution



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1 2

v1

v2

v12,proj

vnew

v12,proj

vnew v12,proj

v1,new

v2,new



from Boltzmann

distribution3 Add/subtract difference of

projected and chosen

velocity to obtain new

velocities



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1 2

v1

v2

v12,proj

vnew

v12,proj

vnew v12,proj

v1,new

v2,new



from Boltzmann

distribution3 Add/subtract difference of

projected and chosen

velocity to obtain new

velocities

Advantage

Conserves linear and angular momentum due to pairwise

correction



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ThermostatsHow to Correct the Velocities?

Usually one particle has more than one neighbour

Lowe-Andersen-1

Take already correctedvelocity

Lowe-Andersen-2

Take original velocityand add up changes

2

4

6

8

10

5000 6000 7000 8000

Temperature

Timesteps

Evolution of Temperature using LA1

Freq = 0.1Freq = 5.0

Freq = 50.0Freq = 100.0

2

4

6

8

10

5000 6000 7000 8000

Temperature

Timesteps

Evolution of Temperature using LA2

Freq = 0.1Freq = 5.0

Freq = 50.0Freq = 100.0



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Parallel StochasticThermostatsPart III: Implementation of the

Lowe-Andersen Thermostat



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Implementation of the Lowe-Andersen ThermostatThe IBIsCO-Code

It is Boltzmann Inversion Software for COarse Graining Simulations

IBIsCO

Code for coarse grainingsimulations

Time propagation with

Leap-Frog-Algorithm

(Verlet-Family)

Boltzmann inversion is

used to calculate the

forces



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Implementation of the Lowe-Andersen ThermostatThe Current Lowe-Andersen Implementation

1 Prepare data for

sending(velocities,

coordinates,

neighbourlist)



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1 Prepare data for

sending(velocities,

coordinates,

neighbourlist)

2 Send data to master

processor



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1 Prepare data for

sending(velocities,

coordinates,

neighbourlist)


processor

3 Correct velocities on

master processor



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1 Prepare data for

sending(velocities,

coordinates,

neighbourlist)


processor


master processor4 Send back velocities



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1 Prepare data for

sending(velocities,

coordinates,

neighbourlist)


processor


master processor

4 Send back velocities

440

450

460

470

480

490

500

0 250 500 750 1000

Temperature

/K

Timesteps

Evolution of Temperatureusing the old Implementation



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Implementation of the Lowe-Andersen ThermostatThe New Implementation of the Lowe-Andersen Thermostat



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1 Correct velocity of pairs

resident on processor



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2 Send remaining pairs to

master processor



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master processor

3 Correct velocities over

boundaries on master

processor



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master processor



processor




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2 Send remaining pairs tomaster processor



processor


440

450

460

470

480

490

500

0 250 500 750 1000

Temperature/K

Timesteps

Evolution of Temperatureusing the new Implementation(red)



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Implementation of the Lowe-Andersen ThermostatScaling of the two methods

160000 particles, 1000 timesteps

1500

1550

1600

1650

8 27 64

Time

/s

# Processors

Scaling of the old Lowe-Andersen Implementation

100

150

200

250

8 27 64

Time

/s

# Processors

Scaling of the new Lowe-Andersen Implementation

#proc.time(old)

/stime(new)

/s8 1588.771 263.700

27 1572.881 115.830

64 1550.005 108.446



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Implementation of the Lowe-Andersen ThermostatMore Ways to Implement the Lowe-Andersen Thermostat Efficiently

1 One processor has 26

neighbours

2 Send data to 13

neighbour cells3 Receive data from other

13 neighbour cells



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neighbours

2 Send data to 13


13 neighbour cells

4 Partially LA2 method



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neighbours

2 Send data to 13


13 neighbour cells

4 Partially LA2 method

5

Equivalent to LA1, ifsending and receiving to

the 13 neighbours is

performed step by step



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t

Thank you for your attention.


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Statistical Thermostats