The fast multipole method (FMM) for electromagnetic scattering problems
- 1 June 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 40 (6), 634-641
- https://doi.org/10.1109/8.144597
Abstract
The fast multipole method (FMM) developed by V. Rokhlin (1990) to efficiently solve acoustic scattering problems is modified and adapted to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet problem for two-dimensional, closed, conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation from O(n/sup 3/) for Gaussian elimination to O(n/sup 4/3/) per conjugate-gradient iteration, where n is the number of sample points on the boundary of the scatterer. A sample technique for accelerating convergence of the iterative method, termed complexifying k, the wavenumber, is also presented. 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(n/sup 4/3/). Computational results for moderate values of ka, where a is the characteristic size of the scatterer, are given.Keywords
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