Section: New Results
Hierarchical Adaptively Restrained Particle Simulations
Participants : Svetlana Artemova, Stephane Redon.
It has been shown that algorithms relying on hierarchical representations of molecular systems may accelerate molecular simulations: for example, divide-and-conquer approach for simulations in internal coordinates [10] , [11] , adaptive algorithms for dynamics of articulated bodies [15] , algorithms for neighbor search for system with symmetries [12] or for large rigid molecules [8] .
Therefore, we were interested in combining hierarchically-based algorithms with Adaptively Restrained Particle Simulations (ARPS). Precisely, as with classical ARPS, we have considered the adaptively restrained (AR) Hamiltonian:
but we have introduced a different form of the inverse inertia matrix
We have performed several numerical experiments to illustrate this new approach. For example, in Fig. 8 we present the planar collision cascade study.
For hierarchical AR simulations, obtained results depend on the tree representation of the system: for the results demonstrated in Fig. 8 the tree was constructed in a top-down manner by recursive dividing of the system in halves and, therefore, the squares of different levels are being activated by the shock.
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To clearly demonstrate the effect of the tree, we provide the results
for the same four simulations with another tree built in a bottom-up
manner by grouping the particles pairwise according to their sequence
number (they were enumerated, first, along the
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The patent reporting the principles and the algorithms used to implement hierarchical ARPS has been deposited.