Title

Towards an adaptive treecode for N-body problems

Document Type

Article

Publication Date

3-5-2020

Department

Department of Mathematical Sciences

Abstract

N-body problems are notoriously expensive to compute. For N bodies, evaluating a sum directly scales like O(N2). A treecode approximation to the N-body problem is highly desirable because for a given level of accuracy, the computation scales instead like O(NlogN). A main component of the treecode approximation, is computing the Taylor coefficients and moments of a cluster–particle approximation. For the two-parameter family of regularized kernels previously introduced (Ong et al. in J Sci Comput 71(3):1212–1237, 2017. https://doi.org/10.1007/s10915-016-0336-0), computing the Taylor coefficients directly is algebraically messy and undesirable. This work derives a recurrence relationship and provides an algorithm for computing the Taylor coefficients of two-parameter family of regularized kernels. The treecode is implemented in Cartesian coordinates, and numerical results verify that the recurrence relationship facilitates computation of Gϵ,n(x) and its derivatives.

Publication Title

Journal of Scientific Computing

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