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The Fast Multipole Method (FMM) for Electromagnetic Scattering Problems
Departmental Papers (ESE)
  • Nader Engheta, University of Pennsylvania
  • William D. Murphy, Rockwell International
  • Vladimir Rokhlin, Yale University
  • Marius S. Vassiliou, Rockwell International Science Center
The fast multipole method (FMM) was developed by Rokhlin to solve acoustic scattering problems very efficiently. We have modified and adapted it to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet (TM) problem for two-dimensional closed conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation (SKIE) from O(n3) for Gaussian elimination to O(n4/3) per conjugated-gradient iteration, where n is the number of sample points on the boundary of the scatterer. We also present a simple technique for accelerating convergence of the iterative method: "complexifying" k, the wavenumber. This has the effect of bounding the condition number of the discrete system; consequently, the operation count of the entire FMM (all iterations) becomes O(n4/3). We present computational results for moderate values of ka, where a is the characteristic size of the scatterer.
Document Type
Journal Article
Date of this Version
Copyright 1992 IEEE. Reprinted from IEEE Transactions on Antennas and Propagation, Volume 40, Issue 6, June 1992, pages 634-641.

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Citation Information
Nader Engheta, William D. Murphy, Vladimir Rokhlin and Marius S. Vassiliou. "The Fast Multipole Method (FMM) for Electromagnetic Scattering Problems" (1992)
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