SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels

Chen, Jeng‐Tzong; Lee, Jia-Wei; Wu, Chi‐Shin; Chen, I‐Lin

doi:10.1016/j.soildyn.2010.12.001

Cited by 58 publications

(14 citation statements)

References 22 publications

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“…The authors of [26] treat a degenerate approximation of the kernel using Taylor series and Lagrange interpolation for solving the general nonlinear Fredholm integro-differential equations under mixed conditions. The degenerate kernel in the polar coordinates for two subdomains is adopted in [9] for the closed-form fundamental solution of null-field boundary integral equation method. Majidiana and Babolian [24] apply a degenerate kernel method with piecewise constant interpolation with respect to the second variable to approximate isolated eigenvalues of a class of noncompact linear operators.…”

Section: Discrete Quasi-interpolant Of Degreementioning

confidence: 99%

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

Mennouni

Zaouia

2017

Math Sci

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Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally, we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature. Moreover, we provide a convergence analysis and we give new error bounds. Finally, we exhibit some numerical examples and compare them with previous results in the literature.

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Section: Discrete Quasi-interpolant Of Degreementioning

confidence: 99%

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

Mennouni

Zaouia

2017

Math Sci

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“…Chen et al (2008) studied the half-plane radiation and scattering problems of multiple alluvial valleys (canyons) using the null-fi eld boundary integral equation method (BIEM), The BIEM is free of calculating the principal values for singular integrals by locating the null-fi eld point exactly on the real boundary. The BIEM has also been successfully extended to study the problem of SH-wave diffraction by a semi-circular hill and a semi-elliptical hill (Chen et al, 2011(Chen et al, , 2012. Note that the above studies only give results for the case of two canyons.…”

Section: Introductionmentioning

confidence: 99%

Scattering and diffraction of plane SH-waves by periodically distributed canyons

Liang

Zhang

2016

Earthq. Eng. Eng. Vib.

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A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green's functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infi nite boundary, and the computational complexity and the demand on memory can be signifi cantly reduced. Furthermore, the total wave fi elds are decomposed into the free fi eld and scattered fi eld in the process of calculation, which means that the method has defi nite physical meaning. The implementation of the method is described in detail and its accuracy is verifi ed. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and signifi cant dynamic interactions exist between the canyons.

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“…However, both methods have limitations in dealing with elastic wave scattering problems in unbounded media containing anisotropic and/or heterogeneous inclusions of arbitrary shapes. It has been demonstrated that a numerical method based on the volume integral equation formulation can overcome such difficulties in solving this class of inclusion problems [2,[4][5][6][7][8]. In contrast to the conventional boundary integral equation method (BIEM), where infinite medium Green's functions for both the matrix and the multilayered anisotropic inclusion are needed, the volume integral equation method (VIEM) does not require the use of Green's function for the multilayered anisotropic inclusion.…”

Section: Introductionmentioning

confidence: 99%

Multiple Scattering Using Parallel Volume Integral Equation Method: Interaction of SH Waves with Multiple Multilayered Anisotropic Elliptical Inclusions

Lee

Jeong

2015

Mathematical Problems in Engineering

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The parallel volume integral equation method (PVIEM) is applied for the analysis of elastic wave scattering problems in an unbounded isotropic solid containing multiple multilayered anisotropic elliptical inclusions. This recently developed numerical method does not require the use of Green’s function for the multilayered anisotropic inclusions; only Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general two- and three-dimensional elastodynamic problems involving inhomogeneous and/or multilayered anisotropic inclusions whose shape and number are arbitrary. A detailed analysis of the SH wave scattering is presented for multiple triple-layered orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces for square and hexagonal packing arrays of triple-layered elliptical inclusions in a broad frequency range of practical interest. It is necessary to use standard parallel programming, such as MPI (message passing interface), to speed up computation in the volume integral equation method (VIEM). Parallel volume integral equation method as a pioneer of numerical analysis enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shape and geometry, isotropy/anisotropy, and softness/hardness of the multiple multilayered anisotropic elliptical inclusions on displacements at the interfaces of the inclusions.

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SH-wave diffraction by a semi-circular hill revisited: A null-field boundary integral equation method using degenerate kernels

Cited by 58 publications

References 22 publications

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

Scattering and diffraction of plane SH-waves by periodically distributed canyons

Multiple Scattering Using Parallel Volume Integral Equation Method: Interaction of SH Waves with Multiple Multilayered Anisotropic Elliptical Inclusions

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