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We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators.
Tree data structures for n-body simulation
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Electrical multipoles and multipole interactions: compact expressions and a diagrammatic method
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Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields
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A hierarchical O(N log N) force-calculation algorithm
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Traceless cartesian tensor forms for spherical harmonic functions: new theorems and applications to electrostatics of dielectric media
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Particle mesh Ewald: An N . log(N) method for Ewald sums in large systems
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A new version of the fast multipole method for the laplace equation in three dimensions
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Meurer, A., Smith, C.P., Paprocki, M., Čertík, O., Kirpichev, S.B., Rocklin, M., Kumar, A., Ivanov, S., Moore, J.K., Singh, S., Rathnayake, T., Vig, S., Granger, B.E., Muller, R.P., Bonazzi, F., Gupta, H., Vats, S., Johansson, F., Pedregosa, F., Curry, M.J., Terrel, A.R., Roučka, v., Saboo, A., Fernando, I., Kulal, S., Cimrman, R., Scopatz, A., 2017 · 2017
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Tinker-hp: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields
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