Accelerating the Discrete Element Method for
Faceted Particles Using HOOMD-Blue
Matthew Spellings, Ryan Marson,
Joshua Anderson, Sharon C. Glotzer
Glotzer Group, University of Michigan
Colloidal and Nanoscale Assembly
Branched
Branched
50 nm
10 nm
Colloidal molecules
200 nm
1μm
500 nm
40 nm
Faceted polyhedra
100 nm
5 nm
100 nm
10μm
300 nm
500 nm
Rods
ellipsoids
Rods and
and ellipsoids
10 nm
2 nm
10 μm
50 nm
100 nm
10 nm
1μm
100 nm
1μm
DOI: 10.1038/nmat1949
5μm
Patterned
Colloidal and Nanoscale Shape
Entropy + Energy →
Assembly
Modelling → predictive
design
DOI: 10.1038/NMAT3178
DOI: 10.1126/science.1220869
Simulating Shape: Monte Carlo
Pure shape
Historically, serial
No dynamics
(nucleation and
growth, active
systems...)
S4166 - Breaking Through Serial
Barriers: Scalable Hard Particle
Monte Carlo Simulations
with HOOMD-Blue
Joshua Anderson, Thursday, 9:00, Room 212A
Active Matter
Emergent Collective Phenomena in a Mixture of
Hard Shapes through Active Rotation
Nguyen, Klotsa, Engel, Glotzer; PRL 2014 - DOI 10.1103/PhysRevLett.112.075701
0:41
Introduction to Molecular Dynamics
→
→
r , velocities v for each particle
→
Positions
i
i
Forces F i calculated from
pairwise/bond/other interactions
Numerically integrate
α
ṙi,
ṗ
α
i,
1
=
α
α −ξ
q̇
i,
mi,
= F i,
α
ṗ
α
(t ,
1
)
α
pi,
ℓ
˙
α
i,
=
α
i,
τ ℓα
+
i,
1
=
2
−1
× Ī
α
Āqi,
ℓα ξ
i,
−
α
(r,
1
)
ℓα
i,
Shape in MD: Stacked Spheres
Easy
Arbitrary
Artifacts?
Performance
Shape in MD: Filling Solution
Optimal Filling of Shapes
Phillips, Anderson, Huber, Glotzer; PRL 2012
DOI 10.1103/PhysRevLett.108.198304
More difficult
Less arbitrary
Fewer artifacts?
(Also)
performance
The Discrete Element Method
Originally developed for granular materials
(corn, sand, soil...)
Integrate forces over time based on contact
points
Typically include friction
Ours: a force computation
method in HOOMD-Blue
Architecture for free
(integrators,
parallelization...)
http://codeblue.umich.edu/hoomd-blue/
2D Discrete Element Contact Forces
Vertex/edge interactions
3D Discrete Element Contact Forces
Vertex/face and edge/edge interactions
Conservative Potentials
Need smooth force field
Steep, purely repulsive potentials
Use nearest point to evaluate force and
torque
2D Parallelization Scheme
Split force components among multiple
threads
Assign two threads per vertex
2D Interaction Calculation
Nearest point between vertex i and edge j
Evaluate conservative potential
3D Parallelization Scheme
Two threads per vertex, one thread per edge
3D Interaction Calculation: Vertex/Face
Nearest point between vertex i and face j
Minimize distance over triangles in face
3D Interaction Calculation: Edge/Edge
Nearest point between edge i and edge j
Performance
Performance
Demo
1:00
Future Work
Multi-CPU, multi-GPU with MPI
Friction
More potentials
Acknowledgments
Glotzer Group
Michael Engel
NSF IGERT - award DGE 0903629
DOE BES-EFRC - award DE-SC0000989
Questions