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spectral element method for the solution of viscoelastic seismic wave propagation

APPLIED NUMERICAL MATHEMATICS 2025年 212卷 92-109页

作者： Barzegar, Feze Rashidinia, Jalil Iran Univ Sci & Technol Sch Math & Comp Sci Tehran Iran

This paper considers the Gauss-Legendre-Lobatto spectral element method combined with the Crank-Nicolson (CN) technique to solve the viscoelastic wave equation model. The CN technique is chosen for its unconditional stability and second-order accuracy. Additionally, the convergence order is determined for the time semi-discrete scheme of the problem. The Gauss-Legendre-Lobatto points are used as interpolation nodes and integral quadrature points to discretize the spatial direction with the spectral element method, providing an a priori estimate. Numerical results demonstrate the proposed method's high efficiency and accuracy.

关键词： Viscoelastic wave equations spectral element method Gauss-Legendre-Lobatto points Error analysis

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A higher-order spectral element method for modeling eccentric anisotropic multilayered waveguides via transformation optics

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INTERNATIONAL JOURNAL OF MICROWAVE AND WIRELESS TECHNOLOGIES 2025年

作者： Ribeiro, Raul O. Rosa, Guilherme S. Bergmann, Jose R. Teixeira, Fernando L. Sao Paulo State Univ UNESP Sch Engn Sao Joao Da Boa Vista SP Brazil Pontif Catholic Univ Rio de Janeiro Dept Elect Engn Rio De Janeiro RJ Brazil Ohio State Univ Electrosci Lab Columbus OH USA

We present a higher-order spectral element method (SEM) for analyzing eccentric anisotropic multilayered waveguides. The formulation uses conformal transformation optics to map the original eccentric waveguide to an equivalent concentric one. This transformation is extended to handle anisotropic non-reciprocal media characterized by non-symmetric and non-Hermitian tensors. In the transformed concentric domain, higher-order two-dimensional basis functions associated with the zeros of the completed Lobatto polynomial are used to expand the fields. To simulate radially unbounded problems, we employ a complex-stretched perfectly matched layer to mimic open space. The method is validated with radially bounded two-layer and three-layer waveguides and radially unbounded three-layer waveguides. Comparisons with the finite element method (FEM) demonstrate that our SEM approach requires significantly fewer degrees of freedom than FEM.

关键词： anisotropic non-reciprocal media eccentric multilayered waveguide spectral element method transformation optics

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Towards the shear-wave sonic reverse time migration with the spectral element method

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JOURNAL OF APPLIED GEOPHYSICS 2025年 233卷

作者： Malovichko, Mikhail Sabitov, Denis Dmitriev, Maxim Zharnikov, Timur Aramco Innovat Moscow Russia EXPEC Adv Res Ctr Saudi Aramco Dhahran Saudi Arabia

This paper evaluates feasibility of three-dimensional sonic reverse-time migration (RTM) based on the spectral element method (SEM). A GPU based algorithm capable of performing both fluid-solid and purely elastic RTM is presented. The key properties of our algorithm is efficient organization of GPU computations, use of optimized unstructured meshes and elements of high order, leveraged with sufficient amount of memory available on newer generations of GPUs. We review the imaging conditions (ICs) for shear-wave imaging, derive four ICs using the Lagrangian formalism and study their merits. We also propose a simple yet powerful approach for automatically constructing unstructured all-hexahedral meshes that respect the borehole geometry. The RTM algorithm's validity and merits are demonstrated through its application on synthetic data as well as a real data set. Overall, our results suggest that the sonic community already possesses the technical capability to perform industrialscale sonic RTM, at least using GPU clusters employing top-tier chips with large global memory.

关键词： Sonic RTM spectral element method

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Vibration characteristics of cylindrical shells with discontinuous connections based on the spectral element method

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2025年 308卷

作者： Chai, Kai Liu, Junfeng Lou, Jingjun Liu, Shuyong Naval Univ Engn Coll Naval Architecture & Ocean Wuhan 430033 Peoples R China Naval Univ Engn Coll Power Engn Wuhan 430033 Peoples R China

Common shell of revolution, such as cylindrical, conical, and spherical shells, are widely used in marine, aerospace, and other engineering fields due to their excellent support and pressure-resistant properties. Research on their vibration characteristics has progressed from single shells to composite shells, from ribbed shells to those with complex internal substructures, and from uniform to discontinuous connections. The discontinuities in wave propagation at the boundaries of discontinuously connected cylindrical shells result in highly complex equation of vibration control, leading to limited studies in this area. This study first models the uniform cylindrical shell and annular plate as spectral elements, using trigonometric and Bessel functions to describe displacement solutions and obtain vibration responses for arbitrary boundary conditions. Then, based on artificial virtual spring theory and the weighted least squares method, the discontinuous connection between the cylindrical shell and annular plate is modeled as a circumferentially varying stiffness distribution, leading to the derivation of dynamic stiffness matrices for both continuous and discontinuous connections. Finite element simulations are conducted using ABAQUS to analyze the vibration characteristics of the discontinuously connected cylindrical shell under free, clamped, and simply supported boundary conditions. Finally, an experimental setup is used to measure the vibration response under harmonic excitation and perform impedance testing with an impact hammer. The results show that the spectral element method accurately calculates the natural frequencies of the stiffened cylindrical shell, with an overall error of less than 2 %, while the maximum error for the experimental shell is 5.8 %.

关键词： Shells of revolution Discontinuous connection spectral element method Artificial virtual spring theory Structural vibration

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Dynamic analysis of liquid-filled clamp-pipe systems based on the spectral element method

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ARCHIVE OF APPLIED MECHANICS 2025年第1期95卷 1-28页

作者： Sun, Zhonghan Yu, Ruyu Wang, Xin Zhang, Xufang Northeastern Univ Sch Mech Engn & Automat Shenyang 110819 Peoples R China China Natl Heavy Duty Truck Grp Co Ltd Automot Res Inst Jinan 250101 Peoples R China Aero Engine Corp China Shenyang Engine Res Inst Shenyang 110015 Peoples R China

This paper presents an effective approach for dynamic analysis of liquid-filled clamp pipe (LFCP) systems based on the spectral element method (SEM). In this regard, six stiffness components are used to represent the elastic supporting effect of a clamp on the pipe structure, and analytical parameters are derived to realize the Rayleigh damping model in the SEM. This determines an SEM-based approach for dynamic analysis of the LFCP system. Numerical verification of the SEM is implemented for natural frequency analysis of the LFCP in conjunction with the straight, the L-shape, and parallel pipe systems. Compared to the finite-element or the transfer-matrix method in the literature, simulation results have confirmed the high accuracy and efficiency of utilizing the SEM for numerical modelling of the LFCP system. Various realizations of the pipe diameter, the fluid density and pressure, and the clamp coefficients are also considered to investigate their combined effects on structural characteristics. It has confirmed that the SEM based approach provides an effective routine for dynamic analysis of the LFCP system.

关键词： The liquid-filled clamp-pipe (LFCP) system spectral element method Natural frequency analysis The Rayleigh damping model

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Flexural wave bandgaps of corrugated-core sandwich metabeam with inertial amplified resonators using the spectral element method

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JOURNAL OF VIBRATION AND CONTROL 2025年第5-6期31卷 904-914页

作者： Li, Xunyu Hu, Yong He, Tao Li, Yinggang Ouyang, Wu Li, Xiaobin Wuhan Univ Technol Key Lab High Performance Ship Technol Minist Educ Wuhan Peoples R China Wuhan Univ Technol Sch Naval Architecture Ocean & Energy Power Engn Dept Naval Architecture Wuhan Peoples R China Wuhan Univ Technol Sch Naval Architecture Ocean & Energy Power Engn Dept Ocean & Struct Engn Wuhan Peoples R China Wuhan Second Ship Design & Res Inst Wuhan Peoples R China Wuhan Univ Technol Sanya Sci & Educ Innovat Pk Sanya Peoples R China Wuhan Univ Technol Sch Transportat & Logist Engn Wuhan Peoples R China Wuhan Univ Technol Key Lab High Performance Ship Technol Minist Educ 1178 Heping Ave Wuhan 430063 Peoples R China Wuhan Univ Technol Sch Transportat & Logist Engn 1178 Heping Ave Wuhan 430063 Peoples R China

In this paper, we present a theoretical investigation of flexural wave propagation and vibration bandgap properties in corrugated-core sandwich metabeam with inertial amplified resonators. The complete analytical solutions for the flexural wave propagation with free boundary conditions are obtained through the spectral element method. Finite element calculation of transmission characteristics of sandwich metabeam with inertial amplified resonators are carried out to validate the accuracy of the proposed complete analytical solutions. In addition, the vibration reduction effect of sandwich metabeam with inertial amplified resonators is compared with that of the corrugated-core metabeam with local resonance. The influences of system parameters on the flexural wave attenuation are analyzed. Results show that the complete analytical solution for the proposed sandwich metabeam structure can be effectively used to predict the vibrational properties. In addition, significant enlargement of low-frequency bandgap can be obtained by using an inertial amplification sandwich metabeam structure. The proposed sandwich metabeam structure has good bandgap adjustment ability.

关键词： inertial amplified resonators corrugated-core sandwich metabeam broadband flexural wave attenuation spectral element method band gaps

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Study on the nonlinear interaction characteristics between rail cracks and ultrasonic based on finite element-spectral element coupling method

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APPLIED ACOUSTICS 2025年 236卷

作者： Xue, Zhiqiang Xu, Yude Hu, Meng Zhu, Xiaoteng Tongji Univ Key Lab Rd & Traff Engn Minist Educ Shanghai 201804 Peoples R China Tongji Univ Shanghai Key Lab Rail Infrastruct Durabil & Syst S Shanghai 201804 Peoples R China Shanghai Inst Technol Sch Railway Transportat Shanghai 201418 Peoples R China Wuxi Inst Technol Sch Management Wuxi 214121 Jiangsu Peoples R China

This study addresses nonlinear ultrasonic wave propagation induced by rail cracks. The domain decomposition theory of finite element-spectral element coupling underpins a computational method that combines the nonlinear effects in the crack region with far-field linear elastic behavior to investigate the nonlinear interactions between cracks and ultrasonic waves. The results show that the nonlinear parameter correlates positively with crack length and angle, reaching its maximum at 6 mm and 90 degrees, approximately 11 times higher than at 0 degrees. The crack angle influences the scattering energy coefficient with a "U-shaped" distribution, showing the highest values at 0 degrees and 90 degrees and lower values between 15 degrees and 60 degrees;at a fixed angle, the scattering energy coefficient increases significantly with crack length. Simulation and experimental errors remain within 5 %, fully validating the numerical results.

关键词： Rail crack Ultrasonic wave Nonlinearity Finite element method spectral element method

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spectral element method for viscoelastic flows in a planar contraction channel

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN FLUIDS 2003年第3期42卷 323-348页

作者： Meng, S Li, XK Evans, G De Montfort Univ Fac Comp Sci & Engn Inst Simulat Sci Leicester LE1 9BH Leics England Chinese Acad Sci Shenyang Inst Automat Shenyang Peoples R China

A new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic fluid flows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four-to-one contraction channel for a fluid governed by an Oldroyd-B constitutive equation. The behaviour of the Oldroyd-B fluids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions. Copyright (C) 2003 John Wiley Sons, Ltd.

关键词： spectral element method viscoelastic flow planar contraction channel an Oldroyd-B fluid

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spectral element method and its application in analysing the vibration band gap properties of two-dimensional square lattices

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JOURNAL OF VIBRATION AND CONTROL 2016年第3期22卷 710-721页

作者： Wu, Zhi-Jing Li, Feng-Ming Harbin Inst Technol Sch Astronaut Wuhan Peoples R China Beijing Univ Technol Coll Mech Engn Beijing 100124 Peoples R China

In this paper, the vibration band gap properties of a two-dimensional square lattice are studied using the spectral element method. Before assembling the spectral equations of whole structures, the spectral stiffness matrices of the tensional and bending elements are established. The frequency responses of the lattices are calculated and compared with those obtained by the finite element method. It can be observed that the results in the spectral element method are more accurate, especially in high frequency ranges. The frequency band gap properties are analyzed based on the accurate frequency responses. The effects of the material and structure parameters on the band gap properties are investigated.

关键词： Frequency response lattice structure sound isolation spectral element method vibration band gap

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spectral element method for wave propagation on irregular domains

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2018年第3期43卷 1-13页

作者： Geng, Yan Hui Qin, Guo Liang Zhang, Jia Zhong Xi An Jiao Tong Univ Sch Energy & Power Engn Xian 710049 Shaanxi Peoples R China

A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss-Lobatto-Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are mapped according to the length scale of the beeline segment or the curve segment. Using the Bubnov-Galerkin method, some acoustic problems with two kinds of irregular domains are simulated in detail. First, the basic problem with analytical solution is analysed numerically. Numerical results show that the SEM integrated with the length-scale method has the same precision as the isoparametric SEM. Also, it can save nearly half of the time cost. Additionally, the acoustic propagations with inlet flow are simulated numerically. All the results indicate that the SEM integrated with the length-scale method has the ability to simulate the acoustic problems with irregular domains. It is shown that the mapping method maintains the curve edges and provides a useful alternative for isoparametric element, which represents a curved edge with a straight edge.

关键词： spectral element method curved quadrilateral element isoparametric element Chebyshev polynomial mapping method

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