2-D Fast Multipole Method -- interactive demo

source (X) target (Y) S (P2M) S|S S|R R|R R (eval)
Algorithm & data
Canvas mode
Animation (upward + downward pass)
Status 

    

  





  
About this demo

  

    A 2-D Coulombic-potential (log kernel) Fast Multipole Method demo, originally written in
    Java by Yang Wang for UMIACS course CMSC 878R / AMSC 698R
    (Fast Multipole Methods, Nail Gumerov and Ramani Duraiswami), first as a
    2003 class project ("Java Implementation and Simulation of the Fast Multipole Method
    for 2-D Coulombic Potential Problems") and extended by 2005 into three Java WebStart
    demos, all still named on the original page one level up
    (../index.htm). Ported to plain JavaScript
    (no dependencies, no build step) 26 Sep 2026.
  

  

    Regular tree ("Regular Multilevel FMM," fmmdemo.zip): a
    single uniform-depth quadtree, chosen so every leaf holds at most the cluster
    threshold's worth of points, following Greengard & Rokhlin, "A fast algorithm for
    particle simulations," J. Comput. Phys. 73(2):325-348 (1987).
  

  

    Adaptive (Cheng-Greengard-Rokhlin) ("Another Adaptive Multilevel FMM,"
    fmmdemo-adaptive2.zip): per-branch quadrant subdivision with four
    classical interaction lists, following Cheng, Greengard & Rokhlin, "A fast adaptive
    multipole algorithm in three dimensions," J. Comput. Phys. 155:468-498 (1999).
  

  

    Adaptive (Gumerov-Duraiswami) ("Adaptive Multilevel FMM,"
    fmmdemo-adaptive.zip): a pruned D-tree of variable-depth target boxes plus
    a companion C-forest supplying the multipole expansions the D-tree needs, following
    N. Gumerov and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in
    Three Dimensions, pp. 265-283, Elsevier Science, Oxford, 2005, Ch. 6 SS6. Its source
    was missing from the internal course archive (only compiled classes survived there) and
    was first reconstructed by decompiling those classes; the real source then turned up in
    fmmdemo-adaptive.zip on this very page and confirmed the reconstruction
    exactly (see NOTES.md).