A multilevel N log N algorithm for solving boundary integral equation

Multilevel algorithms have been used to generate fast algorithms for Fourier transforms and inversion of matrices in finite element method. They usually involve nesting a smaller problem within a larger problem. Recently, multilevel algorithms have been used to solve integral equation by expediting...

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Bibliographic Details
Published inIEEE Antennas and Propagation International Symposium, 1994 Vol. 1; pp. 431 - 434 vol.1
Main Authors Weng Cho Chew, Cai-Cheng Lu
Format Conference Proceeding
LanguageEnglish
Published IEEE 1994
Subjects
Contracts
Finite element methods
Fourier transforms
Integral equations
Interpolation
Iterative algorithms
NASA
Nearest neighbor searches
Scattering
Smoothing methods
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ISBN9780780320093
0780320093
DOI10.1109/APS.1994.407721

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Summary:Multilevel algorithms have been used to generate fast algorithms for Fourier transforms and inversion of matrices in finite element method. They usually involve nesting a smaller problem within a larger problem. Recently, multilevel algorithms have been used to solve integral equation by expediting matrix-vector multiplies or by finding the inverse of the integral operator. Interpolation multilevel algorithm has also been proposed. These algorithms could invert an integral operator in less than O(N/sup 3/) operations and expedite a matrix-vector multiply to require O(Nlog N) or O(N) operations. In this paper, we will describe a multilevel algorithm for expediting matrix-vector multiply in an iterative solution of boundary integral equation. The algorithm has O(N(log N)/sup 2/) complexity, and for very large problem, O(Nlog N) complexity.< >
ISBN:9780780320093
0780320093
DOI:10.1109/APS.1994.407721