Multibody multipole methods
نویسندگان
چکیده
منابع مشابه
Multibody Multipole Methods
A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order n can account for interactions among n-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functi...
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This is a simple introduction to fast multipole methods for the N-body summation problems. Low rank approximation plus hierarchical decomposition leads to fast O(N) or O(N logN) algorithms for the summation problem or equivalently the computation of a matrix-vector product. Code for 1-D problem is presented for a better illustration. We consider a summation problem in the form:
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Besides preserving the energy, the ow of a conservative multibody system possesses important geometric (symplectic) invariants. Symplectic discretization schemes that mimic the corresponding feature of the true ow have been shown to be eeective alternatives to standard methods for many conservative problems. For systems of rigid bodies, the development of such schemes can be complicated or cost...
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We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numerically. We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numericall...
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In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the cost of computing all pairwise interactions in a system of N particles from O(N) to O(N) or O(N logN) operations. They are equally useful, however,...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2012
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2012.06.027