1. Introduction to Scientific Computing II
Molecular Dynamics – Algorithms
Dr. Miriam Mehl

2. Reducing Complexity N particles original costs/time step: O(N2)
task: O(N)
short-range potentials
long-range potential

3. Short-Range Potentials
cut-off radius
interactions/molecule O(1)
integrability condition
corrections

4. Short-Range Potentials

5. Short-Range Potentials

6. Short-Range Potentials

7. Short-Range Potentials

8. Short-Range Potentials
implementation I:
Verlet neighbour lists

9. Short-Range Potentials
implementation II:
Linked-Cell

10. Long-Range Potentials
tree-based methods
integral representation of potentials
distance-dependent far-field subdivision
Taylor expansion of kernel functions

11. Long-Range Potentials

12. Long-Range Potentials
bottom-up calculation
of the moments
kd-trees
octrees

13. Long-Range Potentials
how to
construct the tree
store the tree
choose cells and expansion points
determine far-field and near-field
Barnes-Hut method
fast multipole method