IPAC2015 - List of Authors (Gee, A.J.)

Paper	Title	Page
MOPMA050	Smooth Fast Multipole Method for Space Charge Tracking: An Alternate to Particle-In-Cell	663
	A.J. Gee, B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA B. Erdelyi ANL, Argonne, USA
	The fast multipole method (FMM) algorithm was developed by Greengard and Rokhlin in 1987 . As one of the top ten algorithms of the 20th century, it has been applied in a wide range of fields. The FMM complexity is O(N), where N is the number of articles, allowing for large-scale simulations. However, it includes all the two-body collisional forces, in contrast to other methods such as the popular particle in-cell (PIC) methods. While collisionality can be very important, many applications require only the mean field effects. PIC is frequently used in this regime. Due to recent concerns of unphysical effects of grids, interpolation and other approximations in PIC codes, an alternative based on different underlying assumptions would prove enlightening. For these cases, a smoothed or softened FMM using a Plummer-like smoothing parameter holds much promise. Unfortunately, the original FMM based on analytic expansions of the 1/r-like potentials does not allow for Plummer softening. We present our new soft-FMM employing differential algebras (DA) to obtain the modified expansions. We also compare the performance of the smoothed DA-FMM with examples from PIC simulations. L. Greengard and V. Rokhlin. “A fast algorithm for particle simulations".
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-MOPMA050
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Paper

Title

Page

Smooth Fast Multipole Method for Space Charge Tracking: An Alternate to Particle-In-Cell

663

A.J. Gee, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
B. Erdelyi
ANL, Argonne, USA

The fast multipole method (FMM) algorithm was developed by Greengard and Rokhlin in 1987 *. As one of the top ten algorithms of the 20th century, it has been applied in a wide range of fields. The FMM complexity is O(N), where N is the number of articles, allowing for large-scale simulations. However, it includes all the two-body collisional forces, in contrast to other methods such as the popular particle in-cell (PIC) methods. While collisionality can be very important, many applications require only the mean field effects. PIC is frequently used in this regime. Due to recent concerns of unphysical effects of grids, interpolation and other approximations in PIC codes, an alternative based on different underlying assumptions would prove enlightening. For these cases, a smoothed or softened FMM using a Plummer-like smoothing parameter holds much promise. Unfortunately, the original FMM based on analytic expansions of the 1/r-like potentials does not allow for Plummer softening. We present our new soft-FMM employing differential algebras (DA) to obtain the modified expansions. We also compare the performance of the smoothed DA-FMM with examples from PIC simulations.
* L. Greengard and V. Rokhlin. “A fast algorithm for particle simulations".

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2015-MOPMA050

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)