Error and Complexity Analysis for a Collocation-grid-projection plus Precorrected-fft Algorithm for Solving Potential Integral Equations with Laplace or Helmholtz Kernels

SUMMARY In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected-FFT style multilevel method for solving potential integral equations with 1 r and e ikr =r kernels. A complexity analysis of this combined method is given to show that for homogenous problems, the method is order n log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogenity generated by a very nely discretized surface, the combined method slows to order n 4=3. Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1=r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.