PAC2013 - List of Authors (Abeyratne, S.)

Paper	Title	Page
MOPBA13	Optimization of the Multipole to Local Translation Operator in the Adaptive Fast Multipole Method	201
	S. Abeyratne, B. Erdelyi Northern Illinois University, DeKalb, Illinois, USA B. Erdelyi ANL, Argonne, USA
	The Fast Multipole Method (FMM) is an accurate and fast way to calculate potentials/fields created by a very large number of particles. The run time of the FMM is significantly less than that of the pairwise calculation if the particle number, N is sufficiently large. Two major parts in the FMM are the upward pass and the downward pass. The upward pass calculates multipole expansions and then performs multipole- to-multipole translations. The downward pass calculates multipole-to- local expansions and local-to local expansions. The multipole-to-local translation in the downward pass is the most time consuming translation in the FMM. In order to make the FMM more efficient, we sought to minimize the time taken by the multipole-to-local translation. The promising and practical strategy to minimize the multipole-to-local translation time is to replace the 3D multipole-to-local translation with a 1D multipole-to-local translation in conjunction with rotations of the coordinate axes. In this paper we show how to perform the 1D multipole-to-local translation and the time comparisons between the two FMM variants.

Paper

Title

Page

Optimization of the Multipole to Local Translation Operator in the Adaptive Fast Multipole Method

201

S. Abeyratne, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
B. Erdelyi
ANL, Argonne, USA

The Fast Multipole Method (FMM) is an accurate and fast way to calculate potentials/fields created by a very large number of particles. The run time of the FMM is significantly less than that of the pairwise calculation if the particle number, N is sufficiently large. Two major parts in the FMM are the upward pass and the downward pass. The upward pass calculates multipole expansions and then performs multipole- to-multipole translations. The downward pass calculates multipole-to- local expansions and local-to local expansions. The multipole-to-local translation in the downward pass is the most time consuming translation in the FMM. In order to make the FMM more efficient, we sought to minimize the time taken by the multipole-to-local translation. The promising and practical strategy to minimize the multipole-to-local translation time is to replace the 3D multipole-to-local translation with a 1D multipole-to-local translation in conjunction with rotations of the coordinate axes. In this paper we show how to perform the 1D multipole-to-local translation and the time comparisons between the two FMM variants.