A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
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Publication:693189
DOI10.1007/S11464-012-0188-3zbMATH Open1262.65198arXiv1105.5372OpenAlexW2010717035MaRDI QIDQ693189
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Publication date: 7 December 2012
Published in: (Search for Journal in Brave)
Abstract: An algorithm for the direct inversion of the linear systems arising from Nystrom discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexity when applied to boundary integral equations (BIEs) in the plane with non-oscillatory kernels such as those associated with the Laplace and Stokes' equations. The scaling coefficient suppressed by the "big-O" notation depends logarithmically on the requested accuracy. The method can also be applied to BIEs with oscillatory kernels such as those associated with the Helmholtz and Maxwell equations; it is efficient at long and intermediate wave-lengths, but will eventually become prohibitively slow as the wave-length decreases. To achieve linear complexity, rank deficiencies in the off-diagonal blocks of the coefficient matrix are exploited. The technique is conceptually related to the H and H^2 matrix arithmetic of Hackbusch and co-workers, and is closely related to previous work on Hierarchically Semi-Separable matrices.
Full work available at URL: https://arxiv.org/abs/1105.5372
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