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Fast Updating Multipole Coulombic Potential Calculation



Thomas Hoft, Bradley Alpert


We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position. Errors are bounded even after a large number of such shifts, making it practical for use in Monte Carlo Markov chain methods in molecular dynamics, computational astrophysics, computational chemistry, and other applications. The method uses truncated multipole expansions of the potential and a tree decomposition of the computational domain to reduce the computational complexity. Computational costs scale logarithmically in the size of the problem. Scaling, accuracy, and efficiency are confirmed with numerical experiments. The new method outperforms a direct calculation for moderate problem sizes.
Siam Journal on Scientific Computing


fast multipole method, molecular dynamics, Laplace equation, potential theory, N-body problem


Hoft, T. and Alpert, B. (2017), Fast Updating Multipole Coulombic Potential Calculation, Siam Journal on Scientific Computing, [online],, (Accessed July 13, 2024)


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Created June 5, 2017, Updated October 12, 2021