An algorithm for the direct inversion of the linear systems arising from NystrSm discretization of integral equations on one-dimensional domains is described. The method typically has O（N） complexity when applied to...An algorithm for the direct inversion of the linear systems arising from NystrSm 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 logarithraically on the requested accuracy. The method can also be applied to BIEs with oscillatory kernels such as those associated with the Helmholtz and time-harmonic 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 H2-matrix arithmetic of Hackbusch and coworkers, and is closely related to previous work on Hierarchically Semi-Separable matrices.展开更多
文摘An algorithm for the direct inversion of the linear systems arising from NystrSm 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 logarithraically on the requested accuracy. The method can also be applied to BIEs with oscillatory kernels such as those associated with the Helmholtz and time-harmonic 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 H2-matrix arithmetic of Hackbusch and coworkers, and is closely related to previous work on Hierarchically Semi-Separable matrices.
