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time-accelerated integral equations for twodimensional transient scattering problems

Science in China(Series F) 2003年第1期46卷 1-13页

作者：王建国 Northwest Institute of Nuclear Technology

Based on the Hilbert transform, this paper presents a totally new method to obtain the time-accelerated electric field, magnetic field and combined field integral equations for the two-dimensional transient scattering problems. The computational complexity of the time-accelerated integral equations is analysed, which can be reduced to O(N_s^2NtlogNt) from the conventional O(N_s^2N_t^2). Numerical results verify the computational complexity of this time-accelerated method, and show that the time-accelerated integral equations can provide accurate and stable solutions for both the open and closed objects.

关键词： Hilbert transform march-on-in-time time-accelerated integral equation.

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On hybrid temporal basis functions for stable numerical solution of time domain boundary integral equations

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Advances in Aerodynamics 2019年第1期1卷 184-201页

作者： Fang Q.Hu Department of Mathematics and Statistics Old Dominion UniversityNorfolkVirginiaUSA

Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations,such as the boundary integral *** discretization of integral equations in the time domain often leads to so-called march-on-in-time(MOT)*** the literature,the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis *** order to evaluate the accuracy and effectiveness of the temporal basis functions,a Fourier analysis of the temporal interpolation schemes is carried *** on the Fourier analysis,the spectral resolutions of various temporal basis functions are *** is argued that hybrid temporal basis functions be used for interpolation of the numerical solution and its derivatives with respect to *** of the proposed hybrid schemes is studied by a matrix eigenvalue *** improvement in accuracy and efficiency by using the hybrid temporal basis functions for time domain integral equations is demonstrated by numerical *** with the traditional temporal basis functions,the use of hybrid basis functions keeps numerical errors low for a larger frequency range given the same time step ***,for a given range of frequency of interest,a larger time step can be used with the hybrid temporal basis functions,resulting in an increase in computational efficiency and,at the same time,a reduction in memory requirement.

关键词： time domain integral equation Temporal basis function march-on-in-time

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