The Fast Multipole Method in the Differential Algebra Framework
Abstract
A method is presented that allows the computation of space charge
effects of arbitrary and large distributions of particles in an efficient
and accurate way based on a variant of the Fast Multipole Method (FMM).
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 with a high power of the order. Given an ensemble of N
particles, the method allows the computation of the self-fields of
all particles on each other with a computational expense that scales
as O(N). Using remainder-enhanced DA methods, it is also possible
to obtain rigorous estimates of the errors of the methods. Furthermore,
the method allows the computation of all high-order multipoles of
the space charge fields that are necessary for the computation of
high-order transfer maps and all resulting aberrations.
H. Zhang, M. Berz,
Nuclear Instruments and Methods A645 (2011) 338-344
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