Abstract
We discuss the variable order Fast Multipole Method (FMM) applied to piecewise constant Galerkin discretizations of boundary integral equations. In this version of the FMM low-order expansions are employed in the finest level and orders are increased in the coarser levels. Two versions will be discussed, the first version computes exact moments, the second is based on approximated moments. When applied to integral equations of the second kind, both versions retain the asymptotic error of the direct method. The complexity estimate of the first version contains a logarithmic term while the second version is O(N) where N is the number of panels.
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This work was supported by the NSF under contract DMS-0074553
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Tausch, J. The Variable Order Fast Multipole Method for Boundary Integral Equations of the Second Kind. Computing 72, 267–291 (2004). https://doi.org/10.1007/s00607-004-0063-5
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DOI: https://doi.org/10.1007/s00607-004-0063-5