Geodesic
The fast mulitpole method in the differential algebra framework
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 97-107

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We present a fast multipole method based on differential algebraic methods for the calculation of the self-fields of all charged particles on each other inside a bunch in tracking simulations. It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales geometrically with the order. Different from direct summation, the computational expense scales linear with the particle number. Some simulation results are presented to illustrate the practical performance of the method for realistic problems. Bibliogr. 19. Il. 5. Table 1.
Keywords: space charge effects, fast mulitpole method, differential algebra. 
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H. Zhang; M. Berz. The fast mulitpole method in the differential algebra framework. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 97-107. http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a9/