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Journal articles on the topic 'Stochastic time domain spectral element method'

Author: Grafiati

Published: 6 September 2023

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1

Kronowetter, Felix, Lennart Moheit, Martin Eser, Kian K. Sepahvand, and Steffen Marburg. "Spectral Stochastic Infinite Element Method in Vibroacoustics." Journal of Theoretical and Computational Acoustics 28, no. 02 (June 2020): 2050009. http://dx.doi.org/10.1142/s2591728520500097.

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A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.

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2

Sharma, Himanshu, Shuvajit Mukherjee, and Ranjan Ganguli. "Uncertainty analysis of higher-order sandwich beam using a hybrid stochastic time-domain spectral element method." International Journal for Computational Methods in Engineering Science and Mechanics 21, no. 5 (August 19, 2020): 215–30. http://dx.doi.org/10.1080/15502287.2020.1808912.

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3

Zakian, P., and N. Khaji. "A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain." Meccanica 51, no. 4 (July 24, 2015): 893–920. http://dx.doi.org/10.1007/s11012-015-0242-9.

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4

Beresnev, Igor A., and Gail M. Atkinson. "Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earthquake. I. Validation on rock sites." Bulletin of the Seismological Society of America 88, no. 6 (December 1, 1998): 1392–401. http://dx.doi.org/10.1785/bssa0880061392.

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Abstract The stochastic method of simulating ground motions from finite faults is validated against strong-motion data from the M 6.7 1994 Northridge, California, earthquake. The finite-fault plane is subdivided into elements, each element is assigned a stochastic ω2 spectrum, and the delayed contributions from all subfaults are summed in the time domain. Simulated horizontal acceleration time histories and Fourier spectra at 28 rock sites are compared with observations. We first perform simulations using the slip distribution on the causative fault derived from strong-motion, teleseismic, GPS, and leveling data (Wald et al., 1996). We then test the performance of the method using quasi-random distributions of slip and alternative hypocenter locations; this is important because the rupture initiation point and slip distribution are in general not known for future earthquakes. The model bias is calculated as the ratio of the simulated to the observed spectrum in the frequency band of 0.1 to 12.5 Hz, averaged over a suite of rock sites. The mean bias is within the 95% confidence limits of unity, showing that the model provides an accurate prediction of the spectral content of ground motions on average. The maximum excursion of the model bias from the unity value, when averaged over all 28 rock stations, is a factor of approximately 1.6; at most frequencies, it is below a factor of 1.4. Interestingly, the spectral bias and the standard deviation of the stochastic simulations do not depend on whether the fault slip distribution and hypocenter location are based on data or are randomly generated. This suggests that these parameters do not affect the accuracy of predicting the average characteristics of ground motion, or they may have their predominant effect in the frequency range below about 0.1 Hz (below the range of this study). The implication is that deterministic slip models are not necessary to produce reasonably accurate simulations of the spectral content of strong ground motions. This is fortunate, because such models are not available for forecasting motions from future earthquakes. However, the directivity effects controlled by the hypocenter location are important in determining peak ground acceleration at individual sites. Although the method is unbiased when averaged over all rock sites, the simulations at individual sites can have significant errors (generally a factor of 2 to 3), which are also frequency dependent. Factors such as local geology, site topography, or basin-propagation effects can profoundly affect the recordings at individual stations. To generate more accurate site-specific predictions, empirical responses at each site could be established.

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Li, Xiaozhen, Yan Zhu, and Zhibin Jin. "Nonstationary Random Vibration Performance of Train-Bridge Coupling System with Vertical Track Irregularity." Shock and Vibration 2016 (2016): 1–19. http://dx.doi.org/10.1155/2016/1450895.

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In order to study the random vibration performance of trains running on continuous beam bridge with vertical track irregularity, a time-domain framework of random analysis on train-bridge coupling system is established. The vertical rail irregularity is regarded as a random process. A multibody mass-spring-damper model is employed to represent a moving railway car and the bridge system is simulated by finite elements. By introducing the pseudo excitation algorithm into the train-bridge interaction dynamic system, expressions of the mean value, standard deviation, and power spectral density of the nonstationary random dynamic responses of bridge and vehicles are derived. Monte-Carlo simulations are implemented to validate the presented method. A comprehensive analysis of the train-bridge coupling system with vertical track irregularity is conducted focusing on the effect of the randomness of the vertical rail irregularity on the dynamic behavior of the running train and the three-span continuous concrete bridge. Moreover, stochastic characteristics of the indicator for assessing the safety and the riding quality of the railway cars running on continuous beam bridge are carried out, which may be a useful reference in the dynamic design of the bridge.

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6

Mukherjee, Shuvajit, S. Gopalakrishnan, and Ranjan Ganguli. "Stochastic time domain spectral element analysis of beam structures." Acta Mechanica 230, no. 5 (November 12, 2018): 1487–512. http://dx.doi.org/10.1007/s00707-018-2272-6.

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7

Stavroulakis, G., D. G. Giovanis, V. Papadopoulos, and M. Papadrakakis. "A GPU domain decomposition solution for spectral stochastic finite element method." Computer Methods in Applied Mechanics and Engineering 327 (December 2017): 392–410. http://dx.doi.org/10.1016/j.cma.2017.08.042.

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8

Mukherjee, Shuvajit, S. Gopalakrishnan, and Ranjan Ganguli. "Time domain spectral element-based wave finite element method for periodic structures." Acta Mechanica 232, no. 6 (March 15, 2021): 2269–96. http://dx.doi.org/10.1007/s00707-020-02917-y.

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9

Pind, Finnur, Allan P. Engsig-Karup, Cheol-Ho Jeong, Jan S. Hesthaven, Mikael S. Mejling, and Jakob Strømann-Andersen. "Time domain room acoustic simulations using the spectral element method." Journal of the Acoustical Society of America 145, no. 6 (June 2019): 3299–310. http://dx.doi.org/10.1121/1.5109396.

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10

Lee, Joon-Ho, and Qing Huo Liu. "A 3-D Spectral-Element Time-Domain Method for Electromagnetic Simulation." IEEE Transactions on Microwave Theory and Techniques 55, no. 5 (May 2007): 983–91. http://dx.doi.org/10.1109/tmtt.2007.895398.

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11

Sheng, YiJun, XiaoDong Ye, Gui Wang, and TianYu Lu. "Stability-Improved Spectral-Element Time-Domain Method Based on Newmark-$\beta$." IEEE Microwave and Wireless Components Letters 29, no. 4 (April 2019): 243–45. http://dx.doi.org/10.1109/lmwc.2019.2900842.

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12

Lehikoinen, Antti. "Spectral Stochastic Finite Element Method for Electromagnetic Problems with Random Geometry." Electrical, Control and Communication Engineering 6, no. 1 (October 23, 2014): 5–12. http://dx.doi.org/10.2478/ecce-2014-0011.

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Abstract In electromagnetic problems, the problem geometry may not always be exactly known. One example of such a case is a rotating machine with random-wound windings. While spectral stochastic finite element methods have been used to solve statistical electromagnetic problems such as this, their use has been mainly limited to problems with uncertainties in material parameters only. This paper presents a simple method to solve both static and time-harmonic magnetic field problems with source currents in random positions. By using an indicator function, the geometric uncertainties are effectively reduced to material uncertainties, and the problem can be solved using the established spectral stochastic procedures. The proposed method is used to solve a demonstrative single-conductor problem, and the results are compared to the Monte Carlo method. Based on these simulations, the method appears to yield accurate mean values and variances both for the vector potential and current, converging close to the results obtained by time-consuming Monte Carlo analysis. However, further study may be needed to use the method for more complicated multi-conductor problems and to reduce the sensitivity of the method on the mesh used.

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13

Yin, Changchun, Zonghui Gao, Yang Su, Yunhe Liu, Xin Huang, Xiuyan Ren, and Bin Xiong. "3D Airborne EM Forward Modeling Based on Time-Domain Spectral Element Method." Remote Sensing 13, no. 4 (February 8, 2021): 601. http://dx.doi.org/10.3390/rs13040601.

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Airborne electromagnetic (AEM) method uses aircraft as a carrier to tow EM instruments for geophysical survey. Because of its huge amount of data, the traditional AEM data inversions take one-dimensional (1D) models. However, the underground earth is very complicated, the inversions based on 1D models can frequently deliver wrong results, so that the modeling and inversion for three-dimensional (3D) models are more practical. In order to obtain precise underground electrical structures, it is important to have a highly effective and efficient 3D forward modeling algorithm as it is the basis for EM inversions. In this paper, we use time-domain spectral element (SETD) method based on Gauss-Lobatto-Chebyshev (GLC) polynomials to develop a 3D forward algorithm for modeling the time-domain AEM responses. The spectral element method combines the flexibility of finite-element method in model discretization and the high accuracy of spectral method. Starting from the Maxwell's equations in time-domain, we derive the vector Helmholtz equation for the secondary electric field. We use the high-order GLC vector interpolation functions to perform spectral expansion of the EM field and use the Galerkin weighted residual method and the backward Euler scheme to do the space- and time-discretization to the controlling equations. After integrating the equations for all elements into a large linear equations system, we solve it by the multifrontal massively parallel solver (MUMPS) direct solver and calculate the magnetic field responses by the Faraday's law. By comparing with 1D semi-analytical solutions for a layered earth model, we validate our SETD method and analyze the influence of the mesh size and the order of interpolation functions on the accuracy of our 3D forward modeling. The numerical experiments for typical models show that applying SETD method to 3D time-domain AEM forward modeling we can achieve high accuracy by either refining the mesh or increasing the order of interpolation functions.

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14

Bao, H. G., D. Z. Ding, and R. S. Chen. "A Hybrid Spectral-Element Finite-Difference Time-Domain Method for Electromagnetic Simulation." IEEE Antennas and Wireless Propagation Letters 16 (2017): 2244–48. http://dx.doi.org/10.1109/lawp.2017.2711001.

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15

Joon-Ho Lee, Jiefu Chen, and Qing Huo Liu. "A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 57, no. 9 (September 2009): 2666–74. http://dx.doi.org/10.1109/tap.2009.2027731.

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16

Hu, Zhi Gang, Yong Lin Zhang, Jian Ping Ye, Shao Yun Song, and Li Ping Chen. "Numerical Modeling and Simulation of Random Road Surface Using IFFT Method." Advanced Materials Research 199-200 (February 2011): 999–1004. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.999.

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Based on the power spectral density (PSD) function of stochastic irregularities of the standard grade road and by means of inverse fast Fouerier transform (IFFT) based on discretized PSD sampling, an equivalent sample of stochastic road surface model in time domain was built. A one-dimensional model of stochastic road was developed into a 2D model of stochastic road surface. Through computer simulation practice based on the MATlab, a 2D sample of stochastic road surface in time domain was regenerated. Furthermore, given the sample data, the PSD was estimated and then compared with the theoretical 2D PSD Equation deduced from the one-dimensional PSD expreesion so as to prove the effectiveness and accuracy of the time-domain model regeneration of 2D stochastic road surface by means of IFFT method. The 2D stochastic road surface model directly provided basic road excitation input data for virtual prototyping (VP) and virtual proving ground (VPG) technology.

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17

Chakraborty, Subrata, and Santi Sekhar Dey. "Stochastic Finite Element Simulation of Uncertain Structures Subjected to Earthquake." Shock and Vibration 7, no. 5 (2000): 309–20. http://dx.doi.org/10.1155/2000/730364.

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In present study, the stochastic finite element simulation based on the efficient Neumann expansion technique is extended for the analysis of uncertain structures under seismically induced random ground motion. The basic objective is to investigate the possibility of applying the Neumann expansion technique coupled with the Monte Carlo simulation for dynamic stochastic systems upto that extent of parameter variation after which the method is no longer gives accurate results compared to that of the direct Monte carlo simulation. The stochastic structural parameters are discretized by the local averaging method and then simulated by Cholesky decomposition of the respective covariance matrix. The earthquake induced ground motion is treated as stationary random process defined by respective power spectral density function. Finally, the finite element solution has been obtained in frequency domain utilizing the advantage of Neumann expansion technique.

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18

Xu, Kan, Rushan Chen, Yijun Sheng, Ping Fu, Chuan Chen, Qingshang Yan, and YanYan Yu. "Transient analysis of microwave Gunn oscillator using extended spectral element time domain method." Radio Science 46, no. 5 (September 15, 2011): n/a. http://dx.doi.org/10.1029/2011rs004706.

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19

Jin, Jian-Ming, Mohammad Zunoubi, Kalyan C. Donepudi, and Weng C. Chew. "Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method." Computer Methods in Applied Mechanics and Engineering 169, no. 3-4 (February 1999): 279–96. http://dx.doi.org/10.1016/s0045-7825(98)00158-3.

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20

Zunoubi, M., Jian-Ming Jin, and Weng Cho Chew. "Spectral Lanczos decomposition method for time domain and frequency domain finite-element solution of Maxwell's equations." Electronics Letters 34, no. 4 (1998): 346. http://dx.doi.org/10.1049/el:19980333.

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21

Raja Sekhar, B., S. Gopalakrishnan, and MVVS Murthy. "Wave transmission characteristics for higher-order sandwich panel with flexible core using time-domain spectral element method." Journal of Sandwich Structures & Materials 19, no. 3 (December 5, 2016): 364–93. http://dx.doi.org/10.1177/1099636216664536.

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A new time-domain spectral element with nine degrees of freedom per node is formulated based on higher-order sandwich panel theory, incorporating the flexible behaviour of the core with composite face sheets. Static, free vibrations and wave propagation analysis are carried out using the formulated element. Results obtained using this element are compared with those available in the literature and with commercial finite element codes. The fast convergence of the spectral element method is demonstrated by solving the high-frequency wave propagation problem. A method of computing the wave characteristics, namely wavenumbers and group velocities, in a higher-order sandwich panel is developed using the formulated element. The effect of core damping is studied in detail with different core types, which can be used effectively in sandwich beam design.

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22

Borrel-Jensen, Nikolas, Allan Peter Engsig-Karup, Maarten Hornikx, and Cheol-Ho Jeong. "Accelerated sound propagation using an error-free Fourier method coupled with the spectral-element method." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2731–42. http://dx.doi.org/10.3397/in_2022_0383.

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Simulating acoustics using numerical methods efficiently and accurately has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate the simulations using rectangular decomposition, enabling error-free propagation in the bulk of the domain consisting of air. We exploit the analytical solution to the wave equation calculated using the Fast Fourier Transform with near-optimal spatial and temporal discretizations satisfying the Nyquist criterium. Coupling with the spectral-element method near the boundaries results in a method capable of handling complex geometries with realistic boundaries, though with the caveat that additional errors and computational overhead may result from the interface. This talk will investigate the accuracy and efficiency of the proposed domain decomposition method compared to a spectral-element method running in the entire domain.

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23

Zunoubi, M. R., K. C. Donepudi, Jian-Ming Jin, and Weng Cho Chew. "Efficient time-domain and frequency-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method." IEEE Transactions on Microwave Theory and Techniques 46, no. 8 (1998): 1141–49. http://dx.doi.org/10.1109/22.704957.

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24

Jiang, Tian Hua, and Jing Rong Peng. "Digital Simulation of Bridge Wind Fields Based on Wavelet Method." Advanced Materials Research 201-203 (February 2011): 2532–35. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.2532.

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Digital simulation of stochastic wind velocity field is prerequisite to flutter or buffeting analysis of long-span bridges in time-domain. Wavelet method was applied to the simulation of the stochastic wind field, performing the effective simulation of spatial stochastic wind field. According to the idea of multi-resolution analysis and orthonormal wavelets, relationship between wavelet coefficients and PSD(power spectral density)function is deduced , then the wavelet coefficients on each and every scale are obtained from the given PSD function, the intermittency was introduced into wavelet coefficients while at the same time preserves the target spectral characters. As a result, the inverse wavelet transform is applied to generate stationary wind velocity history through the given wavelet coefficients. A numerical example to illustrate the application of the proposed method for the simulation of a bridge wind velocity ﬁeld is provided.

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25

Galanopoulos, Anastasios, Finnur Pind, Hermes Sampedro Llopis, and Cheol-Ho Jeong. "Binaural reproduction of time-domain spectral element method simulations using spherical harmonic spatial encoding." Journal of the Acoustical Society of America 149, no. 4 (April 2021): A20—A21. http://dx.doi.org/10.1121/10.0004403.

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26

Yu, Zexing, Seyed Hossein Mahdavi, and Chao Xu. "Time-domain Spectral Element Method for Impact Identification of Frame Structures using Enhanced GAs." KSCE Journal of Civil Engineering 23, no. 2 (December 17, 2018): 678–90. http://dx.doi.org/10.1007/s12205-018-0478-8.

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27

Kudela, Paweł, Arkadiusz Żak, Marek Krawczuk, and Wiesław Ostachowicz. "Modelling of wave propagation in composite plates using the time domain spectral element method." Journal of Sound and Vibration 302, no. 4-5 (May 2007): 728–45. http://dx.doi.org/10.1016/j.jsv.2006.12.016.

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28

Fiborek, Piotr, Paweł H. Malinowski, Paweł Kudela, Tomasz Wandowski, and Wiesław M. Ostachowicz. "Time-domain spectral element method for modelling of the electromechanical impedance of disbonded composites." Journal of Intelligent Material Systems and Structures 29, no. 16 (February 27, 2018): 3214–21. http://dx.doi.org/10.1177/1045389x18758193.

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The research focuses on the electromechanical impedance method. The electromechanical impedance method can be treated as non-destructive testing or structural health monitoring approach. It is important to have a reliable tool that allows verifying the integrity of the investigated objects. The electromechanical impedance method was applied here to assess the carbon fibre–reinforced polymer samples. The single and adhesively bonded samples were investigated. In the reported research, the electromechanical impedance spectra up to 5 MHz were considered. The investigation comprised of modelling using spectral element method and experimental measurements. Numerical and experimental spectra were analysed. Differences in spectra caused by differences in considered samples were observed.

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29

Chen, Lizhen, and Chuanju Xu. "A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation." East Asian Journal on Applied Mathematics 3, no. 4 (November 2013): 333–51. http://dx.doi.org/10.4208/eajam.150713.181113a.

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AbstractWe propose and analyse a class of fully discrete schemes for the Cahn-Hilliard equation with Neumann boundary conditions. The schemes combine large-time step splitting methods in time and spectral element methods in space. We are particularly interested in analysing a class of methods that split the original Cahn-Hilliard equation into lower order equations. These lower order equations are simpler and less computationally expensive to treat. For the first-order splitting scheme, the stability and convergence properties are investigated based on an energy method. It is proven that both semi-discrete and fully discrete solutions satisfy the energy dissipation and mass conservation properties hidden in the associated continuous problem. A rigorous error estimate, together with numerical confirmation, is provided. Although not yet rigorously proven, higher-order schemes are also constructed and tested by a series of numerical examples. Finally, the proposed schemes are applied to the phase field simulation in a complex domain, and some interesting simulation results are obtained.

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30

Liu, Youshan, Jiwen Teng, Haiqiang Lan, Xiang Si, and Xueying Ma. "A comparative study of finite element and spectral element methods in seismic wavefield modeling." GEOPHYSICS 79, no. 2 (March 1, 2014): T91—T104. http://dx.doi.org/10.1190/geo2013-0018.1.

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The computational accuracy and efficiency of finite element method and spectral element method (SEM) are investigated thoroughly in time-domain elastic wavefield modeling. The diagonal mass matrices of the FEM and SEM free from matrix inversion are compared comprehensively by making full use of the mass-lumped technique and quadrature rules. We investigate the FEM and SEM based, respectively, on quadrilateral with the polynomials of degrees one and two, and on triangular grids with the polynomials of degrees one and three. Generally, the numerical solutions based on quadrilateral grids have a higher precision than those computed on triangular grids when the same order of polynomials is used. The FEM has a comparable accuracy to the SEM with the same number of interpolant points. In view of the triangular and quadrilateral SEMs, the former suffers from larger computational costs and relatively lower accuracy compared with the latter. Furthermore, the convergence study proves that the triangular SEM produces consistently larger errors than the quadrilateral SEM for any order and element sizes. However, the triangular SEM can adapt to arbitrary complex geometries effectively. In terms of efficiency, the FEM has an efficiency comparable with the SEM on condition that the order of interpolation polynomials is identical. In addition, a perfectly matched layer (PML) boundary condition in variational form is deduced. By introducing four intermediate variables in frequency domain, the PML avoids convolution calculation and obtains an exact solution through inverse Fourier transform in time domain. The numerical examples verify the validity and effectiveness of the PML.

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31

Sun, Qingtao, Runren Zhang, Qiwei Zhan, and Qing Huo Liu. "3-D Implicit–Explicit Hybrid Finite Difference/Spectral Element/Finite Element Time Domain Method Without a Buffer Zone." IEEE Transactions on Antennas and Propagation 67, no. 8 (August 2019): 5469–76. http://dx.doi.org/10.1109/tap.2019.2913740.

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32

Lamrhari, D., D. Sarsri, and M. Rahmoune. "Component mode synthesis and stochastic perturbation method for dynamic analysis of large linear finite element with uncertain parameters." Journal of Mechanical Engineering and Sciences 14, no. 2 (June 22, 2020): 6753–69. http://dx.doi.org/10.15282/jmes.14.2.2020.17.0529.

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In this paper, a method to calculate the first two moments (mean and variance) of the stochastic time response as well as the frequency functions of large FE models with probabilistic uncertainties in the physical parameters is proposed. This method is based on coupling of second order perturbation method and component mode synthesis methods. Various component mode synthesis methods are used to optimally reduce the size of the model. The analysis of dynamic response of stochastic finite element system can be done in the frequency domain using the frequency transfer functions and in the time domain by a direct integration of the equations of motion, using numerical procedures. The statistical first two moments of dynamic response of the reduced system are obtained by the second order perturbation method. Numerical applications have been developed to highlight effectiveness of the method developed to analyze the stochastic response of large structures.

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33

Huang, Xin, Changchun Yin, Colin G. Farquharson, Xiaoyue Cao, Bo Zhang, Wei Huang, and Jing Cai. "Spectral-element method with arbitrary hexahedron meshes for time-domain 3D airborne electromagnetic forward modeling." GEOPHYSICS 84, no. 1 (January 1, 2019): E37—E46. http://dx.doi.org/10.1190/geo2018-0231.1.

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Mainstream numerical methods for 3D time-domain airborne electromagnetic (AEM) modeling, such as the finite-difference (FDTD) or finite-element (FETD) methods, are quite mature. However, these methods have limitations in terms of their ability to handle complex geologic structures and their dependence on quality meshing of the earth model. We have developed a time-domain spectral-element (SETD) method based on the mixed-order spectral-element (SE) approach for space discretization and the backward Euler (BE) approach for time discretization. The mixed-order SE approach can contribute an accurate result by increasing the order of polynomials and suppress spurious solutions. The BE method is an unconditionally stable technique without limitations on time steps. To deal with the rapid variation of the fields close to the AEM transmitting loop, we separate a secondary field from the primary field and simulate the secondary field only, for which the primary field is calculated in advance. To obtain a block diagonal mass matrix and hence minimize the number of nonzero elements in the system of equations to be solved, we apply Gauss-Lobatto-Legendre integral techniques of reduced order. A direct solver is then adopted for the system of equations, which allows for efficient treatment of the multiple AEM sources. To check the accuracy of our SETD algorithm, we compare our results with the semianalytical solution for a layered earth model. Then, we analyze the modeling accuracy and efficiency for different 3D models using deformed physical meshes and compare them against results from 3D FETD codes, to further show the flexibility of SETD for AEM forward modeling.

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34

Jiefu Chen, Joon-Ho Lee, and Qing Huo Liu. "A High-Precision Integration Scheme for the Spectral-Element Time-Domain Method in Electromagnetic Simulation." IEEE Transactions on Antennas and Propagation 57, no. 10 (October 2009): 3223–31. http://dx.doi.org/10.1109/tap.2009.2028633.

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35

Kim, Yujun, Sungwon Ha, and Fu-Kuo Chang. "Time-Domain Spectral Element Method for Built-In Piezoelectric-Actuator-Induced Lamb Wave Propagation Analysis." AIAA Journal 46, no. 3 (March 2008): 591–600. http://dx.doi.org/10.2514/1.27046.

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36

Ostachowicz, W., and P. Kudela. "Wave propagation numerical models in damage detection based on the time domain spectral element method." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012068. http://dx.doi.org/10.1088/1757-899x/10/1/012068.

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37

Bottero, Alexis, Paul Cristini, Dimitri Komatitsch, and Mark Asch. "An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics." Journal of the Acoustical Society of America 140, no. 5 (November 2016): 3520–30. http://dx.doi.org/10.1121/1.4965964.

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38

Sheng, Yijun, Kan Xu, Daoxiang Wang, and Rushan Chen. "Performance analysis of FET microwave devices by use of extended spectral-element time-domain method." International Journal of Electronics 100, no. 5 (May 2013): 699–717. http://dx.doi.org/10.1080/00207217.2012.720947.

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39

Yu, Zexing, Chao Xu, Fei Du, Shancheng Cao, and Liangxian Gu. "Time-domain Spectral Finite Element Method for Wave Propagation Analysis in Structures with Breathing Cracks." Acta Mechanica Solida Sinica 33, no. 6 (June 3, 2020): 812–22. http://dx.doi.org/10.1007/s10338-020-00170-3.

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40

Thiery, Florian, Sudhakar Gantasala, and Jan-Olov Aidanpää. "Numerical evaluation of multilobe bearings using the spectral method." Advances in Mechanical Engineering 9, no. 7 (July 2017): 168781401770713. http://dx.doi.org/10.1177/1687814017707135.

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Hydropower rotors and pumps have the specificity to be oriented vertically, meaning that the bearing forces have to be evaluated at each time-step depending on the position of the rotor for dynamical analyses. If the bearing forces cannot be evaluated analytically, a suitable numerical method should be used to calculate the pressure distribution over the bearing domain. This process can be computationally expensive as it should be performed for each discrete time-step. As a result, a comparison between the spectral method, the finite difference method, and the finite element method is performed to investigate which method is more adapted to dynamical analysis of the bearing. It is observed that the spectral method has the advantage of having a reasonable simulation time for any eccentricity magnitude with a moderate number of interpolation points. However, this method should be restricted to simple bearing models such as plain bearings or multilobe bearings due to the advantage of finding a global numerical solution directly on the entire bearing/pad domain.

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Huang, D. "Stochastic fm models and non-linear time series analysis." Advances in Applied Probability 29, no. 4 (December 1997): 986–1003. http://dx.doi.org/10.2307/1427850.

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An important model in communications is the stochastic FM signal st = A cos , where the message process {mt} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt} is a Gaussian MA (q) sequence. The spectral density of {St} can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St} is asymptotically strictly stationary if {mt} is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt}. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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Rizzi, S. A., and J. F. Doyle. "A Spectral Element Approach to Wave Motion in Layered Solids." Journal of Vibration and Acoustics 114, no. 4 (October 1, 1992): 569–77. http://dx.doi.org/10.1115/1.2930300.

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A matrix methodology similar to that of the finite element method is developed for the analysis of stress waves in layered solids. Because the mass distribution is modeled exactly, the approach gives the exact frequency response of each layer. The fast Fourier transform and Fourier series are used for inversion to the time/space domain. The impact of a structured medium with multiple layers is used to demonstrate the method. Comparison with existing propagator and direct global matrix methods show the present approach to be computationally more efficient.

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Pranowo, Pranowo, and Djoko Budiyanto Setyohadi. "Numerical simulation of electromagnetic radiation using high-order discontinuous galerkin time domain method." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (April 1, 2019): 1267. http://dx.doi.org/10.11591/ijece.v9i2.pp1267-1274.

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<span>In this paper, we propose the simulation of 2-dimensional electromagnetic wave radiation using high-order discontinuous Galerkin time domain method to solve Maxwell's equations. The domains are discretized into unstructured straight-sided triangle elements that allow enhanced flexibility when dealing with complex geometries. The electric and magnetic fields are expanded into a high-order polynomial spectral approximation over each triangle element. The field conservation between the elements is enforced using central difference flux calculation at element interfaces. Perfectly matched layer (PML) boundary condition is used to absorb the waves that leave the domain. The comparison of numerical calculations is performed by the graphical displays and numerical data of radiation phenomenon and presented particularly with the results of the FDTD method. Finally, our simulations show that the proposed method can handle simulation of electromagnetic radiation with complex geometries easily.</span>

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Bai, Quan, Zi Xin Liu, Jing Jing Han, Sheng Ji Jin, and He Yu. "Application of Wavelet Transform in Stochastic Loading Characteristics Analysis." Applied Mechanics and Materials 488-489 (January 2014): 662–65. http://dx.doi.org/10.4028/www.scientific.net/amm.488-489.662.

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Understanding the characteristics of stochastic loading is the premise and foundation for structure analysis. Traditional amplitude spectrum and power spectral density (PSD) method based on Fourier transform (FT) has limitation, that is, it loses any information with time and can not reflect the non-stationary characteristics of stochastic loading. Wavelet transform possesses assembling ability in both time and frequency domain,and it possess stronger ability of analyzing non-stationary signal. In this paper, the method of estimating PSD and time-dependent PSD of stochastic loading using wavelet transform is researched. The calculating process is programmed and the method is validated by a numerical example. The analysis result of example indicates that the method presented in this paper is feasible.

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Huang, D. "Stochastic fm models and non-linear time series analysis." Advances in Applied Probability 29, no. 04 (December 1997): 986–1003. http://dx.doi.org/10.1017/s0001867800047984.

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An important model in communications is the stochastic FM signal st = A cos , where the message process {m t} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt } is a Gaussian MA (q) sequence. The spectral density of {St } can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St } is asymptotically strictly stationary if {m t } is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt }. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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Nanda, Namita. "Spectral finite element method for wave propagation analysis in smart composite beams containing delamination." Aircraft Engineering and Aerospace Technology 92, no. 3 (January 29, 2020): 440–51. http://dx.doi.org/10.1108/aeat-02-2019-0026.

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Purpose The purpose of the study is to present a frequency domain spectral finite element model (SFEM) based on fast Fourier transform (FFT) for wave propagation analysis of smart laminated composite beams with embedded delamination. For generating and sensing high-frequency elastic waves in composite beams, piezoelectric materials such as lead zirconate titanate (PZT) are used because they can act as both actuators and sensors. The present model is used to investigate the effects of parametric variation of delamination configuration on the propagation of fundamental anti-symmetric wave mode in piezoelectric composite beams. Design/methodology/approach The spectral element is derived from the exact solution of the governing equation of motion in frequency domain, obtained through fast Fourier transformation of the time domain equation. The beam is divided into two sublaminates (delamination region) and two base laminates (integral regions). The delamination region is modeled by assuming constant and continuous cross-sectional rotation at the interfaces between the base laminate and sublaminates. The governing differential equation of motion for delaminated composite beam with piezoelectric lamina is obtained using Hamilton’s principle by introducing an electrical potential function. Findings A detailed study of the wave response at the sensor shows that the A0 mode can be used for delamination detection in a wide region and is more suitable for detecting small delamination. It is observed that the amplitude and time of arrival of the reflected A0 wave from a delamination are strongly dependent on the size, position of the delamination and the stacking sequence. The degraded material properties because of the loss of stiffness and density in damaged area differently alter the S0 and A0 wave response and the group speed. The present method provides a potential technique for researchers to accurately model delaminations in piezoelectric composite beam structures. The delamination position can be identified if the time of flight of a reflected wave from delamination and the wave propagation speed of A0 (or S0) mode is known. Originality/value Spectral finite element modeling of delaminated composite beams with piezoelectric layers has not been reported in the literature yet. The spectral element developed is validated by comparing the present results with those available in the literature. The spectral element developed is then used to investigate the wave propagation characteristics and interaction with delamination in the piezoelectric composite beam.

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Chen, Shitao, Dazhi Ding, and Rushan Chen. "A Hybrid Volume–Surface Integral Spectral-Element Time-Domain Method for Nonlinear Analysis of Microwave Circuit." IEEE Antennas and Wireless Propagation Letters 16 (2017): 3034–37. http://dx.doi.org/10.1109/lawp.2017.2759147.

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Qian, Cheng, Dazhi Ding, Zhenhong Fan, and Rushan Chen. "A fluid model simulation of a simplified plasma limiter based on spectral-element time-domain method." Physics of Plasmas 22, no. 3 (March 2015): 032111. http://dx.doi.org/10.1063/1.4916055.

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Mokhtari, Ali, Hamid Reza Mirdamadi, Mostafa Ghayour, and Vahid Sarvestan. "Time/wave domain analysis for axially moving pre-stressed nanobeam by wavelet-based spectral element method." International Journal of Mechanical Sciences 105 (January 2016): 58–69. http://dx.doi.org/10.1016/j.ijmecsci.2015.11.006.

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Schulte, Rolf T., Ke Jia Xing, and Claus Peter Fritzen. "Spectral Element Modelling of Wave Propagation and Impedance Based SHM Systems." Key Engineering Materials 413-414 (June 2009): 683–90. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.683.

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In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.

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