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DOE OSTI · 1610846

An adaptive fast multipole method in Cartesian basis, enabled by algorithmic differentiation

Abeyratne, S.·Gee, A.·Erdelyi, B.
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Abstract

A novel form of the fast multipole method is realized by the combination of adaptive data structures with implementation of the multipole expansions and their translations in Cartesian basis, and enabled by algorithmic differentiation. It may be possible to generalize it to any kernel that allows its formulation as a function of small quantities with respect to which they can be expanded. There is no hard and fast rule recipe that works for all cases. However, it is shown how to do it for the softened Coulomb kernel, which is different from the Coulomb kernel. The characteristics and performance of the method are mapped and shown to provide an attractive option for a generic fast multipole algorithm in a wide region of the parameter space. The algorithm is illustrated with a beam dynamics application.

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97 MATHEMATICS AND COMPUTINGadaptive fast multipole methodbeam dynamicsdifferential algebrasoftened Coulomb kernel

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Abeyratne, S., Gee, A., Erdelyi, B.. 2019-01-03. An adaptive fast multipole method in Cartesian basis, enabled by algorithmic differentiation. https://doi.org/10.1016/j.cnsns.2019.01.001

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