Comparing precorrected-FFT and fast multipole algorithms for solving three-dimensional potential integral equations

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:224493

White, J; Phillips, J R; Korsmeyer, T ^[1]

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1. Massachusetts Institute of Technology, Cambridge, MA (United States)

Mixed first- and second-kind surface integral equations with (1/r) and {partial_derivative}/{partial_derivative} (1/r) kernels are generated by a variety of three-dimensional engineering problems. For such problems, Nystroem type algorithms can not be used directly, but an expansion for the unknown, rather than for the entire integrand, can be assumed and the product of the singular kernal and the unknown integrated analytically. Combining such an approach with a Galerkin or collocation scheme for computing the expansion coefficients is a general approach, but generates dense matrix problems. Recently developed fast algorithms for solving these dense matrix problems have been based on multipole-accelerated iterative methods, in which the fast multipole algorithm is used to rapidly compute the matrix-vector products in a Krylov-subspace based iterative method. Another approach to rapidly computing the dense matrix-vector products associated with discretized integral equations follows more along the lines of a multigrid algorithm, and involves projecting the surface unknowns onto a regular grid, then computing using the grid, and finally interpolating the results from the regular grid back to the surfaces. Here, the authors describe a precorrectted-FFT approach which can replace the fast multipole algorithm for accelerating the dense matrix-vector product associated with discretized potential integral equations. The precorrected-FFT method, described below, is an order n log(n) algorithm, and is asymptotically slower than the order n fast multipole algorithm. However, initial experimental results indicate the method may have a significant constant factor advantage for a variety of engineering problems.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 224493
• Report Number(s): CONF-9404305--Vol.1; ON: DE96005735
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
COMPARATIVE EVALUATIONS
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FOURIER ANALYSIS
INTEGRAL EQUATIONS
MATRICES
THREE-DIMENSIONAL CALCULATIONS