# A Fully Traceless Cartesian Multipole Formulation for the Distributed Fast Multipole Method

@article{Coles2018AFT, title={A Fully Traceless Cartesian Multipole Formulation for the Distributed Fast Multipole Method}, author={Jonathan P. Coles and Rebekka Bieri}, journal={arXiv: Computational Physics}, year={2018} }

We present efficient operators for the fast multipole method (FMM) based on totally symmetric and traceless Cartesian multipole tensors, which have been designed to translate well into computer code. Using the traceless tensor form significantly reduces memory usage and network communication traffic for large-scale applications in molecular dynamics and astrophysics. We have also developed a software generator that symbolically produces, verifies, and optimizes code for the FMM operators. The…

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fmmgen: Automatic Code Generation of Operators for Cartesian Fast Multipole and Barnes-Hut Methods

- Computer Science
- 2020

This paper details the implementation and testing of a software package, fmmgen, in which the source code for Barnes-Hut and Fast Multipole operator functions for calculating calculate the potential, field or both from arbitrary ordered sources is easily generated through symbolic algebra.

## References

SHOWING 1-10 OF 18 REFERENCES

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

- Computer ScienceJ. Comput. Phys.
- 2018

A fast multipole method for stellar dynamics

- Biology
- 2014

This work out-performs a GPU-based direct summation with comparable force errors for N≳105 and employs a novel estimate for the errors incurred in this process to minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors.

A new version of the fast multipole method for screened Coulomb interactions in three dimensions

- Computer Science
- 2002

A new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2 + 6p3 operations per box.

The fast multipole method and point dipole moment polarizable force fields.

- PhysicsThe Journal of chemical physics
- 2015

The expected O(N) scaling of the fast multipole method is demonstrated by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid and the long time energy conservation in molecular dynamics at the nanosecond scale is shown.

Optimizing the Accuracy and Efficiency of Fast Hierarchical Multipole Expansions for MD Simulations.

- Computer ScienceJournal of chemical theory and computation
- 2012

The correctness of the present SAMMp implementation is demonstrated by analyzing the scaling of the residuals and by checking the numerical accuracy of the reaction principle for a pair of distant molecular ions in vacuum.

Electrical multipoles and multipole interactions: compact expressions and a diagrammatic method

- Chemistry
- 1981

Compact expressions for the calculation of electric multipoles, multipole interactions, potentials, fields and field gradients created by multipoles and force constants between multipoles have been…

A Hierarchical O(N) Force Calculation Algorithm

- Computer Science, Physics
- 2002

A novel code for the approximate computation of long-range forces between N mutually interacting bodies is presented. The code is based on a hierarchical tree of cubic cells and features mutual…

Accelerated Cartesian expansions - A fast method for computing of potentials of the form R-ν for all real ν

- Computer ScienceJ. Comput. Phys.
- 2007

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields

- Chemistry
- 1984

Traceless cartesian tensor forms for spherical harmonic functions: new theorems and applications to electrostatics of dielectric media

- Mathematics
- 1989

A solid spherical harmonic of degree n at a point r takes the tensor contraction form A(n).n.rn, where A(n) is a totally symmetric and traceless nth-rank cartesian tensor. The utility of this form…