UMD CMSC 878R - A kernel-independent adaptive fast multipole algorithm in two and three dimensions (36 pages)

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A kernel-independent adaptive fast multipole algorithm in two and three dimensions



Previewing pages 1, 2, 17, 18, 19, 35, 36 of actual document.

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A kernel-independent adaptive fast multipole algorithm in two and three dimensions

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Pages:
36
School:
University of Maryland, College Park
Course:
Cmsc 878r - Advanced Topics In Numerical Methods

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Journal of Computational Physics 196 2004 591 626 www elsevier com locate jcp A kernel independent adaptive fast multipole algorithm in two and three dimensions q Lexing Ying George Biros Denis Zorin Courant Institute of Mathematical Sciences New York University New York 10012 USA Received 17 July 2003 received in revised form 6 November 2003 accepted 11 November 2003 Abstract We present a new fast multipole method for particle simulations The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations Instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical FMM tree we use a continuous distribution of an equivalent density on a surface enclosing the box To nd this equivalent density we match its potential to the potential of the original sources at a surface in the far eld by solving local Dirichlet type boundary value problems The far eld evaluations are sparsi ed with singular value decomposition in 2D or fast Fourier transforms in 3D We have tested the new method on the single and double layer operators for the Laplacian the modi ed Laplacian the Stokes the modi ed Stokes the Navier and the modi ed Navier operators in two and three dimensions Our numerical results indicate that our method compares very well with the best known implementations of the analytic FMM method for both the Laplacian and modi ed Laplacian kernels Its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels 2003 Elsevier Inc All rights reserved Keywords Fast multipole methods Fast solvers Integral equations Single layer potential Double layer potential Particle methods N body problems 1 Introduction Many methods in computational physics e g vortex methods molecular dynamics are based on the evolution of particle systems with pairwise interactions corresponding to



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