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Theses

Incremental Algorithm for long range interactions

Abstract : Particle simulations have become an essential tool in various fields such as physics, astrophysics, biology, chemistry, climatology, and engineering, to name few. Usually, these computer simulations produce a temporal evolution of the system of interest by describing the motion of particles.In order to perform reliable simulations, we must provide an accurate description of interaction forces undergone by each particle. In most cases, these forces mirror inter-particle interactions and depend on relative coordinates of the particles. Moreover, pairwise long-range interactions are generally the cornerstone of particle simulations, an example being gravitational forces that are so essential in astrophysics. In molecular simulations, coulombic forces between electrically charged complexes are the most common illustration of long-range interactions.Furthermore, due to their computational cost, pairwise long-range interactions are the bottleneck of particle simulations. Therefore, sophisticated algorithms must be used for efficient evaluations of these interactions.In this thesis, we thus propose so-called << incremental >> algorithms which may significantly reduce the cost of long-range interactions when the studied system is governed by a particular dynamics. Precisely, these algorithms are effective for simulations where a part of the system remains frozen awhile. In particular, our algorithms will be validated on systems whose particles are governed by the so-called Adaptively Restrained Molecular Dynamics (ARMD) which is a promising approach in molecular dynamics simulations.'Although several incremental algorithms introduced by this thesis will be devoted to molecular dynamics simulations, we believe that they can be generalized to all kinds of long-range interactions.
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Semeho Edorh. Incremental Algorithm for long range interactions. Computer Arithmetic. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAM047⟩. ⟨tel-01980307v2⟩

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