Technische Universität MünchenDepartment of Informatics V

13.11.2015

Philipp Neumann, Nikola Tchipev

Short range interaction,Linked Cell algorithm

PSE Molekulardynamik

2

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Outline

• Schedule• Presentations: Worksheet 2• Short range interaction• Linked-cell algorithm• Preparation: Worksheet 3

3

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Schedule

Date Worksheet

16.10.2015

30.10.2015 1

13.11.2015 2

04.12.2015 3

18.12.2015 4

22.01.2016 5

4

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Presentations: Worksheet 2

5

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Revision: Lennard-Jones potential

• Interaction between molecules or atoms

• Resulting force calculation

6

• Dense force matrix

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Revision: Lennard-Jones potential

Idea: Neglect near zero forces

⇒ complexity:

7

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Short range interaction

8

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Short range interaction

9

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Verlet lists

• Each molecule → list of neighboring molecules depending on

• List update every time steps

⇒ buffer with:

10

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Linked-cell algorithm (classic)

• Introduction of a Cartesian (cubic spatial) mesh

• Mesh size given by cut-off radius

• Newton’s third law: Iterate only over neighboring cells

• Natural application of existing particle containers (sheet 3)

• Domain decomposition parallelization? (sheet 5)⇒

11

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Linked-cell algorithm (outlook)

• Cubic mesh with side length:

• Converges to cut-off sphere for

12

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Linked-cell algorithm: Data structure

Linearized array (2D/3D→1D) Mesh: 1D vector of cells Cells: list of molecules Halo region: boundary

conditions/ghost layer Outflow: delete molecules after

time step (sheet 3) Reflecting boundaries Periodic BCs? (sheet 4) Distributed memory parallelization?

13

Technische Universität MünchenDepartment of Informatics V

Philipp Neumann, Nikola Tchipev PSE Molekulardynamik

Preparation: Worksheet 3