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

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

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)

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) ( http://lammps.sandia.gov/ ) runs on a single processor or in parallel distributed-memory message-passing parallelism (MPI) spatial-decomposition of simulation domain for parallelism

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!

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)

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)

Benchmarking of LAT parallel algorithm Soft beads with Box of size: 40x40x40 Time step: Time taken for 10000 steps K. R. Prathyusha et al., Proceedings of the ATIP/A*CRC workshop-2012, 124 (2012)

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)

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