Introduction to Scientific Computing II Molecular Dynamics – Algorithms Dr. Miriam Mehl Institut für Informatik Scientific Computing In Computer Science

Reducing Complexity N particles  original costs/time step: O(N 2 )  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

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

bottom-up calculation of 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 calculation of the moments  kd-trees  octrees MAXI M MAXIMILIAN