A fast multipole accelerated indirect boundary element method for broadband scattering of elastic waves in a fluid‐saturated poroelastic domain

Liu, Zhongxian; Sun, Shanzhong; Cheng, Alexander H.‐D.; Wang, Yirui

doi:10.1002/nag.2848

Cited by 9 publications

(5 citation statements)

References 63 publications

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“…In this research, the fast multipole method (FMM) (Makarov et al ., 2018; Qu et al ., 2017, 2018; Takahashi et al ., 2017) is exerted to couple with the LIBEM as the new method, FM-LIBEM, which can be used for large-scale computation. The FMM has been applied in many fields by coupling with other mathematic methods since its invention, like acoustic analysis (Chen et al ., 2019a, b), elasticity analysis (Liu et al ., 2018; Rezaei et al ., 2019; Wang et al ., 2017a) and electromagnetic analysis (Ahmad and Kasilingam, 2019; Ren et al ., 2017). The proposed FM-LIBEM in this research can enhance computation efficiency without losing accuracy generally.…”

Section: Introductionmentioning

confidence: 99%

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

Liu,

Wang,

Feng

et al. 2023

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Purpose3D steady heat conduction analysis considering heat source is conducted on the fundamental of the fast multipole method (FMM)-accelerated line integration boundary element method (LIBEM).Design/methodology/approachDue to considering the heat source, domain integral is generated in the traditional heat conduction boundary integral equation (BIE), which will counteract the well-known merit of the BEM, namely, boundary-only discretization. To avoid volume discretization, the enhanced BEM, the LIBEM with dimension reduction property is introduced to transfer the domain integral into line integrals. Besides, owing to the unsatisfactory performance of the LIBEM when it comes to large-scale structures requiring massive computation, the FMM-accelerated LIBEM (FM-LIBEM) is proposed to improve the computation efficiency further.FindingsAssuming N and M are the numbers of nodes and integral lines, respectively, the FM-LIBEM can reduce the time complexity from O(NM) to about O(N+ M), and a full discussion and verification of the advantage are done based on numerical examples under heat conduction.Originality/value(1) The LIBEM is applied to 3D heat conduction analysis with heat source. (2) The domain integrals can be transformed into boundary integrals with straight line integrals by the LIM. (3) A FM-LIBEM is proposed and can reduce the time complexity from O(NM) to O(N+ M). (4) The FM-LIBEM with high computational efficiency is exerted to solve 3D heat conduction analysis with heat source in massive computation successfully.

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Section: Introductionmentioning

confidence: 99%

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

Liu,

Wang,

Feng

et al. 2023

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“…Results showed that the parameters of incoming stress waves, model boundary conditions, and roadway dimensions have significant effects on the dynamic behaviors of surrounding rock. 13,[20][21][22][23] Additionally, field studies and physical model tests were carried out with an emphasis on the deformation and failure of underground roadways. It was discovered that the surrounding rock of the underground roadway primarily showed radial fracture under the action of stress wave, and the failure modes were greatly influenced by the incoming direction of stress waves, the stress level of the surrounding rock, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Based on numerical simulation techniques, many researchers analyzed the dynamic stress distribution, micro deformation, and macro failure of surrounding rock subjected to dynamic disturbance. Results showed that the parameters of incoming stress waves, model boundary conditions, and roadway dimensions have significant effects on the dynamic behaviors of surrounding rock 13,20–23 . Additionally, field studies and physical model tests were carried out with an emphasis on the deformation and failure of underground roadways.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of dynamic stress distribution around a circular damaged roadway under transient disturbance

Zhao,

Tao,

2023

Num Anal Meth Geomechanics

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Excavation damaged zone (EDZ) widely exists in the surrounding rock of underground roadway due to blasting excavation, which can further change the surrounding rock property and deteriorate the stability of the roadway. In the presented research, a damaged roadway model was developed to investigate the dynamic stress concentration factor (DSCF) distribution around the damaged roadway under a transient plane P wave. The influencing factors on DSCF distribution were discussed, including the shear modulus (μe/μd) of the intact surrounding rock to that of the damaged surrounding rock, the thickness of EDZ (Rd/R0), and the wavelength of the incident stress wave. Results indicated that the damaged surrounding rock around the roadway belongs to stress‐relaxed zones, and the existence of EDZ can reduce the overall DSCF of surrounding rock. As the ratio of μe/μd is increasing, both the maximum compressive and tensile stress concentrations in the damaged zones decrease gradually, which is opposite to that in the intact surrounding rock. A larger EDZ can induce a higher DSCF in the damaged surrounding rock and a smaller DSCF in the intact surrounding rock. As the incident stress wave's wavelength is increasing, the peak value of DSCF grows first before declining, finally followed by a constant value. Furthermore, the maximum compressive and tensile stress concentrations are always found near the surrounding rock that is perpendicular to and along the incoming direction of stress waves, respectively. The stress concentration in both intact and damaged surrounding rock near the incoming side of stress waves is higher than that at the transmitted side.

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“…The numerical methods include finite difference method (FDM) 24–29 . finite element method (FEM), 30–32 boundary element method (BEM), 33–40 discrete wave number method, and other boundary‐type or hybrid methods. More related papers can be found in the literature review 41 …”

Section: Introductionmentioning

confidence: 99%

Indirect boundary element method for modelling 2‐D poroelastic wave diffraction by cavities and cracks in half space

Sun

Liu

Cheng

2021

Num Anal Meth Geomechanics

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An indirect boundary element method (IBEM) is developed to solve two‐dimensional (2‐D) wave diffraction by cavities and cracks in a fluid‐saturated poroelastic half space. The dynamic Green's functions of forces and fluid source in a poroelastic full‐space, rather than their half‐space counterparts, are utilized, because of their closed‐form expressions. The diffracted wave field is constructed by distributing forces and sources in fictitious densities over the boundaries, based on the single‐layer potential theory. The densities are determined by matching the approximate solution with the boundary conditions. The nonuniqueness of integral equation caused by the degenerated geometry of a crack is treated by a zoned approach. The numerical accuracy and stability of the IBEM are verified by comparing with available results in the literature. Problems of wave scattering by cavity and flat crack in saturated half plane are solved. The displacement amplification effect on the free surface is investigated. The numerical solutions show that the response is strongly dependent on factors such as wave frequency, incident angle, the length and depth of the crack, and material properties.

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A fast multipole accelerated indirect boundary element method for broadband scattering of elastic waves in a fluid‐saturated poroelastic domain

Cited by 9 publications

References 63 publications

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

Theoretical analysis of dynamic stress distribution around a circular damaged roadway under transient disturbance

Indirect boundary element method for modelling 2‐D poroelastic wave diffraction by cavities and cracks in half space

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