1. Formulation of an algorithm to implement Lowe-Andersen thermostat in parallel molecular simulation package, LAMMPS
Prathyusha K. R. and P. B. Sunil Kumar
Complex Fluids and Biological Physics Lab
Department of Physics
IIT Madras

2. Introduction
Molecular Dynamic (MD) Simulation solves Newton’s equations of motion
 Microcanonical NVE ensemble
NVT is more realistic than an NVE ensemble:
Various thermostat used in MD simulations:
Nose-Hoover thermostat
Andersen thermostat
Stochastic Dynamics thermostat
Dissipative Particle Dynamics thermostat
Lowe-Andersen thermostat

3. Lowe-Andersen thermostat (LAT)
A thermostat with momentum conservation
Simulates a wide-range of Schmidt number,
Kinematic viscosity
Diffusion coefficient
For water,
Method
Step 1: Solve for positions and velocities of particles at
Step 2: For all pairs of particles within
(zero mean and unit variance)
Generate a relative velocity from a distribution
and
with a probability
C. P. Lowe, Europhys. Lett. 47, 145 (1999)

4. Single CPU simulation Soft beads in a box of size: 15x15x15
Number density:
Time step:
Co-ordinates of particle
Elements of stress tensor
Volume of the box
To simulate millions of particles: LAMMPS
(Large-scale Atomic/Molecular Massively Parallel Simulator)
S. Plimpton, J Comp Phys, 117, 1 (1995)
( )
runs on a single processor or in parallel
distributed-memory message-passing parallelism (MPI)
spatial-decomposition of simulation domain for parallelism

5. Parallelization of LAT is difficult due to the pair update of velocity
Domain 1.
Domain 3.
Domain 4.
Domain 2.
Spatial decomposition assign particle to each domain
Each processor update position, velocities and compute forces
Communication scheme for particles in nearby boxes
Ghost particles  particles which aren’t part of a domain but interacting with that domain.
Parallelization of LAT is difficult due to the pair update of velocity
This update scheme requires the velocity of neighbor particles
Processors should know the updated velocity of particle at the instant.
A processor a priori don’t know a particle at the boundary is involved in collision
Velocity has to be communicated every time, when there is a collision between particles. It is computationally expensive!

6. A modified algorithm for LAT
Communicate and update velocity after few collision events
Pick up no. of pairs randomly for collision
No. of boundary particles
This ensure that is uniformly distributed within each domain
Velocity is updated using the LAT Eqn.
The parameter that controls :
(no. of communication at given time step)
The mapping between original LAT:
( Total no. of pairs in each domain)
The parameter that defines the probability
K. R. Prathyusha et al., Proceedings of the ATIP/A*CRC workshop-2012, 124 (2012)

7. Validating LAT parallel algorithm
Soft beads in a box of size: 15x15x15
does not change with the
number of processors for given
The relation between and
The relationship between
(original LAT) and : linear
(No. of processor used 16)
K. R. Prathyusha et al., Proceedings of the ATIP/A*CRC workshop-2012, 124 (2012)

8. Benchmarking of LAT parallel algorithm
Soft beads with
Box of size: 40x40x40
Time step:
Time taken for steps
K. R. Prathyusha et al., Proceedings of the ATIP/A*CRC workshop-2012, 124 (2012)

9. Few applications of modified LAT
Polymer Dynamics Simulations
Living Polymer Simulations
K. R. Prathyusha et al., Proceedings of the ATIP/A*CRC workshop-2012, 124 (2012)

10. Thank you for your attention
Conclusions
A parallel version of Lowe-Andersen thermostat was developed
Its suitability by comparing the original serial version
with the modified parallel version, is validated
Viscosity parameter in the original and modified versions of LAT
exhibit linear relation
The algorithm is shown to exhibit good scaling
with the number of processors
Acknowledgments
HPCE, at IIT Madras
Thank you for your attention