TY - JOUR
T1 - A fast multipole method for the three-dimensional Stokes equations
AU - Tornberg, Anna Karin
AU - Greengard, Leslie
N1 - Funding Information:
L.G. acknowledges support from DOE Grant DE-FG02-88ER25053. A.K.T. acknowledges support from NSF grant DMS-0412203 and an Alfred P. Sloan Research Fellowship. A.K.T. is also a Royal Swedish Academy of Sciences Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation.
PY - 2008/1/10
Y1 - 2008/1/10
N2 - Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145-149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468-498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.
AB - Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145-149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468-498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.
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U2 - 10.1016/j.jcp.2007.06.029
DO - 10.1016/j.jcp.2007.06.029
M3 - Article
AN - SCOPUS:37249064654
SN - 0021-9991
VL - 227
SP - 1613
EP - 1619
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 3
ER -