Integral equation-based coupled electromagnetic-circuit simulation in the frequency domain

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.

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Integral Equation for Dynamic Poroelasticity in Frequency Domain with BEM Solution

Journal of Engineering Mechanics ◽

10.1061/(asce)0733-9399(1991)117:5(1136) ◽

1991 ◽

Vol 117 (5) ◽

pp. 1136-1157 ◽

Cited By ~ 133

Author(s):

Alexander H.‐D. Cheng ◽

Taoreed Badmus ◽

Dimitri E. Beskos

Keyword(s):

Integral Equation ◽

Frequency Domain

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On the applicability of a renormalized Born series for seismic wavefield modelling in strongly scattering media

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz105 ◽

2019 ◽

Vol 17 (2) ◽

pp. 277-299 ◽

Cited By ~ 1

Author(s):

Xingguo Huang ◽

Morten Jakobsen ◽

Ru-Shan Wu

Keyword(s):

Integral Equation ◽

Frequency Domain ◽

Large Scale ◽

Integral Equation Method ◽

Equation Method ◽

Scattering Media ◽

Matrix Vector Multiplication ◽

Born Series ◽

And Inversion ◽

Matrix Vector

Abstract Scattering theory is the basis for various seismic modeling and inversion methods. Conventionally, the Born series suffers from an assumption of a weak scattering and may face a convergence problem. We present an application of a modified Born series, referred to as the convergent Born series (CBS), to frequency-domain seismic wave modeling. The renormalization interpretation of the CBS from the renormalization group prospective is described. Further, we present comparisons of frequency-domain wavefields using the reference full integral equation method with that using the convergent Born series, proving that both of the convergent Born series can converge absolutely in strongly scattering media. Another attractive feature is that the Fast Fourier Transform is employed for efficient implementations of matrix–vector multiplication, which is practical for large-scale seismic problems. By comparing it with the full integral equation method, we have verified that the CBS can provide reliable and accurate results in strongly scattering media.

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Fundamental Solutions of Poroelastodynamics in Frequency Domain Based on Wave Decomposition

Journal of Applied Mechanics ◽

10.1115/1.4023692 ◽

2013 ◽

Vol 80 (6) ◽

Cited By ~ 9

Author(s):

Boyang Ding ◽

Alexander H.-D. Cheng ◽

Zhanglong Chen

Keyword(s):

Integral Equation ◽

Wave Field ◽

Frequency Domain ◽

Compressional Wave ◽

Fundamental Solutions ◽

Point Force ◽

Wave Fields ◽

Wave Effects ◽

Wave Decomposition ◽

2D And 3D

Fundamental solutions of poroelastodynamics in the frequency domain have been derived by Cheng et al. (1991, “Integral Equation for Dynamic Poroelasticity in Frequency Domain With BEM Solution,” J. Eng. Mech., 117(5), pp. 1136–1157) for the point force and fluid source singularities in 2D and 3D, using an analogy between poroelasticity and thermoelasticity. In this paper, a formal derivation is presented based on the decomposition of a Dirac δ function into a rotational and a dilatational part. The decomposition allows the derived fundamental solutions to be separated into a shear and two compressional wave components, before they are combined. For the point force solution, each of the isolated wave components contains a term that is not present in the combined wave field; hence can be observable only if the present approach is taken. These isolated wave fields may be useful in applications where it is desirable to separate the shear and compressional wave effects. These wave fields are evaluated and plotted.

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The Influnce of Velocity for a Moving Load on the Vibration Isolation Using Pile Group

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.204-208.210 ◽

2012 ◽

Vol 204-208 ◽

pp. 210-214

Author(s):

Man Qing Xu ◽

Bin Xu

Keyword(s):

Integral Equation ◽

Fundamental Solution ◽

Frequency Domain ◽

Half Space ◽

Vibration Isolation ◽

Moving Load ◽

Free Field ◽

Isolation Effect ◽

Moving Loads ◽

Patch Load

Based on Biot’s theory and integral transform method, the velocity of moving loads impact on the vibration isolation effect of pile rows embedded in a poroelastic half space is investigated in this study. The free field solution for a moving load applied on the surface of a poroelastic half space and the fundamental solution for a harmonic circular patch load applied in the poroelastic half space are derived first. Using Muki’s method and the fundamental solution for the circular patch load as well as the obtained free field solution for the moving load, the second kind of Fredholm integral equation in the frequency domain describing the dynamic interaction between pile rows and the poroelastic half space is developed. Numerical solution of the frequency domain integral equation and numerical inversion of the Fourier transform yield the time domain response of the pile-soil system. Numerical results of this study show that the same pile rows can achieve a better vibration isolation effect for the lower load speed than for the higher speed. Also, the optimal length of piles for higher speed moving loads is shorter than that for lower speed moving loads.

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