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Computational Software: Simple FMM Libraries for Electrostatics, Slow Viscous Flow, and Frequency-Domain Wave Propagation

Published online by Cambridge University Press:  30 July 2015

Zydrunas Gimbutas  and
Leslie Greengard
Zydrunas Gimbutas*
Affiliation:
Information Technology Laboratory, National Institute of Standards and Technology, 325 Broadway, Mail Stop 891.01, Boulder, CO 80305-3328, USA
Leslie Greengard
Affiliation:
Simons Center for Data Analysis, Simons Foundation, 160 Fifth Avenue, NY, NY 10010, USA Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110, USA
*
*Corresponding author. Email addresses: [email protected] (Z. Gimbutas), [email protected] (L. Greengard)
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Abstract

We have developed easy to use fast multipole method (FMM) libraries for the Laplace, low-frequency Helmholtz, and Stokes equations in two and three dimensions. The codes are based on a new method for applying translation operators and provide reasonable performance on either single core processors, or small multi-core systems using OpenMP.

Keywords

52B1065D1868U0568U07Fast multipole methodLaplace equationHelmholtz equationStokes equationlayer potentialsprojection-based point and shoot translation operators
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 2 , August 2015 , pp. 516 - 528
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Carrier, J., Greengard, L., and Rokhlin, V., A Fast Adaptive Multipole Algorithm for Particle Simulations, SIAM J. Sci. and Stat. Comput., 9 (1988), 669–686.Google Scholar
[2]Drake, J. B., Worley, P. and D’Azevedo, E., Spherical Harmonic Transform Algorithms, ACM Trans. Math. Softw., 35 (2008), 111–126.Google Scholar
[3]Cheng, H., Greengard, L. and Rokhlin, V., A Fast Adaptive Multipole Algorithm in Three Dimensions, J. Comput. Phys., 155 (1999), 468–498.Google Scholar
[4]Cheng, H., Crutchfield, W. Y., Gimbutas, Z., Greengard, L., Ethridge, F., Huang, J., Rokhlin, V., Yarvin, N., and Zhao, J., A wideband Fast Multipole Method for the Helmholtz equation in three dimensions, J. Comput. Phys., 216 (2006), 300–325.Google Scholar
[5]Chew, W. C., Recurrence relations for three-dimensional scalar addition theorem, J. Electromagnet. Waves Appl. 6 (1992), 133–142.Google Scholar
[6]Crutchfield, W., Gimbutas, Z., Greengard, L., Huang, J., Rokhlin, V., Yarvin, N., and Zhao, J., Remarks on the implementation of the wideband FMM for the Helmholtz equation in two dimensions, Contemporary Mathematics, 408 (2006), 99–110.Google Scholar
[7]Darve, E. and Havé, P., Efficient Fast Multipole Method for Low-Frequency Scattering, J. Comput. Phys., 197 (2004), 341–363.CrossRefGoogle Scholar
[8]Happel, J. and Brenner, H. (1973). Low Reynolds Number Hydrodynamics, 2nd ed., Noordhoff International Publishing, Leyden, Netherlands.Google Scholar
[9]Gimbutas, Z. and Greengard, L. (2012). FMMLIB2 - Fast Multipole Method (FMM) library for the evaluation of potential fields governed by the Laplace and Helmholtz equations in R 2, http://www.cims.nyu.edu/cmcl/fmm2dlib/fmm2dlib.html.Google Scholar
[10]Gimbutas, Z. and Greengard, L. (2012). FMMLIB3 - Fast Multipole Method (FMM) library for the evaluation of potential fields governed by the Laplace and Helmholtz equations in R 3, http://www.cims.nyu.edu/cmcl/fmm3dlib/fmm3dlib.html.Google Scholar
[11]Gimbutas, Z. and Greengard, L. (2012). STFMMLIB3 - Fast Multipole Method (FMM) library for the evaluation of potential fields governed by the Stokes equations in R 3, http://www.cims.nyu.edu/cmcl/fmm3dlib/fmm3dlib.html.Google Scholar
[12]Gimbutas, Z. and Greengard, L., Translation of multipole expansions via projection, in preparation.Google Scholar
[13]Greengard, L. and Huang, J., A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions, J. Comput. Phys., 180 (2002), 642–658.Google Scholar
[14]Greengard, L. and Rokhlin, V., A New Version of the Fast Multipole Method for the Laplace Equation in Three Dimensions, Acta Numerica (1997), 229–269.Google Scholar
[15]Gumerov, N. A. and Duraiswami, R., Recursions for the computation of multipole translation and rotation coefficients for the 3-D Helmholtz equation, SIAM J. Sci.Comput., 25 (2003), 1344–1381.Google Scholar
[16]Pozrikidis, C. (1992). Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
[17]Tornberg, A.-K. and Greengard, L., A fast multipole method for the three-dimensional Stokes equations. J. Comput. Phys., 227 (2008), 1613–1619.Google Scholar
[18]Wang, H., Lei, T., Li, J., Huang, J., Yao, Z., A parallel fast multipole accelerated integral equation scheme for 3D Stokes equations. Int. J. Num. Meth. Eng., 70 (2007), 812–839.Google Scholar
[19]White, C. A. and Head-Gordon, M., Rotating around the quartic angular momentum barrier in fast multipole method calculations, J. Chem. Phys. 105 (1996), 5061–5067.CrossRefGoogle Scholar
[20]Xu, Y., Electromagnetic scattering by an aggregate of spheres, Appl. Opt., 34 (1995), 4573–4588Google Scholar