A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Wavelet Galerkin Algorithms for Boundary Integral Equations
SIAM Journal on Scientific Computing
Variable order panel clustering
Computing
Improving Error Bounds for Multipole-Based Treecodes
SIAM Journal on Scientific Computing
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
A fast numerical solution method for two dimensional Fredholm integral equations of the second kind
Applied Numerical Mathematics
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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.