The Fast Multipole Method in the Differential Algebra Framework
AbstractA 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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