Introduction to Scientific Computing II

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Introduction to Scientific Computing II
Introduction to Scientific Computing II
Introduction to Scientific Computing II
Introduction to Scientific Computing II
Introduction to Scientific Computing II
Introduction to Scientific Computing II
Introduction to Scientific Computing II
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Presentation transcript:

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

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 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

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