Introduction to Scientific Computing II

Molecular Dynamics – Algorithms

Dr. Miriam Mehl

Institut fürInformatik

Scientific ComputingIn Computer Science

Reducing Complexity

• N particles

original costs/time step: O(N2)

task: O(N)

• short-range potentials

• long-range potential

Short-Range Potentials

• cut-off radius

interactions/molecule O(1)

• integrability condition

• corrections

Short-Range Potentials

Short-Range Potentials

Short-Range Potentials

Short-Range Potentials

Short-Range Potentials

implementation I:

Verlet neighbour lists

Short-Range Potentials

implementation II:

Linked-Cell

Long-Range Potentials

• tree-based methods

integral representation of potentials

• distance-dependent far-field subdivision

• Taylor expansion of kernel functions

Long-Range Potentials

Long-Range Potentials

bottom-up calculationof the moments

kd-trees octrees

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

Long-Range Potentials

bottom-up calculationof the moments

kd-trees octrees

MAXI MMAXIMILIAN