IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v412y2022ics0096300321006482.html
   My bibliography  Save this article

Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions

Author

Listed:
  • Chai, Yingbin
  • Li, Wei
  • Liu, Zuyuan

Abstract

To improve the performance of the low-order linear triangular element for solving transient wave propagation problems, this paper presents a novel enriched finite element method (EFEM) for wave analysis. The original linear nodal shape functions are enriched by using the additional interpolation cover functions over patches of elements. To effectively solve the wave problems, the used interpolation cover function is constructed by using the Lagrangian functions plus the harmonic trigonometric functions. The present approach can be regarded as a combination of the classical finite elements and the spectral techniques, but individual strengths of the two methods are synergized, so more accurate results can be obtained compared to the standard finite elements. In this work the root of the linear dependence (LD) issue in the present EFEM is investigated detailedly, and then an effective approach is proposed to completely eliminate the LD problem. By performing the dispersion analysis, it is found that the present EFEM possesses the attractive monotonic convergence property for transient wave propagations, that is the obtained numerical solutions will monotonically converge to the exact solutions with the decreasing time steps for time integration as long as the reasonably fine meshes are used. Several typical numerical examples are solved to illustrate the capacities of the present method.

Suggested Citation

  • Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006482
    DOI: 10.1016/j.amc.2021.126564
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321006482
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126564?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Y. & Liu, G.R., 2019. "A novel node-based smoothed finite element method with linear strain fields for static, free and forced vibration analyses of solids," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 30-58.
    2. S.M. Dsouza & T. Khajah & X Antoine & S.P.A. Bordas & S. Natarajan, 2021. "Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 27(1), pages 263-294, January.
    3. You, Xiangyu & Li, Wei & Chai, Yingbin, 2020. "A truly meshfree method for solving acoustic problems using local weak form and radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    4. Xi, Qiang & Fu, Zhuojia & Wu, Wenjie & Wang, Hui & Wang, Yong, 2021. "A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Dariush Khezrimotlagh & Yao Chen, 2018. "The Optimization Approach," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 107-134, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gui, Qiang & Li, Wei & Chai, Yingbin, 2023. "The enriched quadrilateral overlapping finite elements for time-harmonic acoustics," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Liyuan Lan & Suifu Cheng & Xiatao Sun & Weiwei Li & Chao Yang & Fajie Wang, 2022. "A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    3. Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    4. Jue Qu & Hao Guo & Hongjun Xue & Sina Dang & Yingchun Chen, 2022. "Experimental Study on Manned/Unmanned Thermal Environment in Radar Electronic Shelter Based on Different Air Supply Conditions," Energies, MDPI, vol. 15(4), pages 1-29, February.
    5. Tingting Sun & Peng Wang & Guanjun Zhang & Yingbin Chai, 2022. "A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    6. Dongdong Liu & Xing Wei & Chengbin Li & Chunguang Han & Xiaxi Cheng & Linlin Sun, 2022. "Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    7. Li, Yancheng & Liu, Cong & Li, Wei & Chai, Yingbin, 2023. "Numerical investigation of the element-free Galerkin method (EFGM) with appropriate temporal discretization techniques for transient wave propagation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    8. Yingbin Chai & Kangye Huang & Shangpan Wang & Zhichao Xiang & Guanjun Zhang, 2023. "The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    9. Cong Liu & Shaosong Min & Yandong Pang & Yingbin Chai, 2023. "The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media," Mathematics, MDPI, vol. 11(3), pages 1-27, January.
    10. Xunbai Du & Sina Dang & Yuzheng Yang & Yingbin Chai, 2022. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis," Mathematics, MDPI, vol. 10(23), pages 1-27, December.
    11. Lin Chen & Wenzhi Xu & Zhuojia Fu, 2022. "A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    12. Jue Qu & Hongjun Xue & Yancheng Li & Yingbin Chai, 2022. "An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    13. Xingxing Yue & Buwen Jiang & Xiaoxuan Xue & Chao Yang, 2022. "A Simple, Accurate and Semi-Analytical Meshless Method for Solving Laplace and Helmholtz Equations in Complex Two-Dimensional Geometries," Mathematics, MDPI, vol. 10(5), pages 1-9, March.
    14. Sina Dang & Gang Wang & Yingbin Chai, 2023. "A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    15. Cheng Chi & Fajie Wang & Lin Qiu, 2023. "A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    16. Yang Zhang & Qiang Gui & Yuzheng Yang & Wei Li, 2022. "The Instability and Response Studies of a Top-Tensioned Riser under Parametric Excitations Using the Differential Quadrature Method," Mathematics, MDPI, vol. 10(8), pages 1-23, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qu, Wenzhen & Sun, Linlin & Li, Po-Wei, 2021. "Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 347-357.
    2. Wang, Yongli & Wang, Yudong & Huang, Yujing & Yang, Jiale & Ma, Yuze & Yu, Haiyang & Zeng, Ming & Zhang, Fuwei & Zhang, Yanfu, 2019. "Operation optimization of regional integrated energy system based on the modeling of electricity-thermal-natural gas network," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    3. Yang, Lin & Pang, Shujiang & Wang, Xiaoyan & Du, Yi & Huang, Jieyu & Melching, Charles S., 2021. "Optimal allocation of best management practices based on receiving water capacity constraints," Agricultural Water Management, Elsevier, vol. 258(C).
    4. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    5. Wang, Yongli & Li, Jiapu & Wang, Shuo & Yang, Jiale & Qi, Chengyuan & Guo, Hongzhen & Liu, Ximei & Zhang, Hongqing, 2020. "Operational optimization of wastewater reuse integrated energy system," Energy, Elsevier, vol. 200(C).
    6. Changyu Zhou & Guohe Huang & Jiapei Chen, 2019. "A Type-2 Fuzzy Chance-Constrained Fractional Integrated Modeling Method for Energy System Management of Uncertainties and Risks," Energies, MDPI, vol. 12(13), pages 1-21, June.
    7. Hu, Lin & Hu, Xiaosong & Che, Yunhong & Feng, Fei & Lin, Xianke & Zhang, Zhiyong, 2020. "Reliable state of charge estimation of battery packs using fuzzy adaptive federated filtering," Applied Energy, Elsevier, vol. 262(C).
    8. Hao, Ran & Lu, Tianguang & Ai, Qian & Wang, Zhe & Wang, Xiaolong, 2020. "Distributed online learning and dynamic robust standby dispatch for networked microgrids," Applied Energy, Elsevier, vol. 274(C).
    9. Li, Yang & Wang, Bin & Yang, Zhen & Li, Jiazheng & Chen, Chen, 2022. "Hierarchical stochastic scheduling of multi-community integrated energy systems in uncertain environments via Stackelberg game," Applied Energy, Elsevier, vol. 308(C).
    10. Qiaohua Fang & Xuezhe Wei & Haifeng Dai, 2019. "A Remaining Discharge Energy Prediction Method for Lithium-Ion Battery Pack Considering SOC and Parameter Inconsistency," Energies, MDPI, vol. 12(6), pages 1-24, March.
    11. Ming Zhang & Qianwen Huang & Sihan Liu & Huiying Li, 2019. "Multi-Objective Optimization of Aircraft Taxiing on the Airport Surface with Consideration to Taxiing Conflicts and the Airport Environment," Sustainability, MDPI, vol. 11(23), pages 1-27, November.
    12. Ruidi Chen & Ioannis Ch. Paschalidis, 2022. "Robust Grouped Variable Selection Using Distributionally Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1042-1071, September.
    13. Darya Pyatkina & Tamara Shcherbina & Vadim Samusenkov & Irina Razinkina & Mariusz Sroka, 2021. "Modeling and Management of Power Supply Enterprises’ Cash Flows," Energies, MDPI, vol. 14(4), pages 1-17, February.
    14. Kumar Jadoun, Vinay & Rahul Prashanth, G & Suhas Joshi, Siddharth & Narayanan, K. & Malik, Hasmat & García Márquez, Fausto Pedro, 2022. "Optimal fuzzy based economic emission dispatch of combined heat and power units using dynamically controlled Whale Optimization Algorithm," Applied Energy, Elsevier, vol. 315(C).
    15. Mohammed Abdullah H. Alshehri & Youguang Guo & Gang Lei, 2023. "Energy Management Strategies of Grid-Connected Microgrids under Different Reliability Conditions," Energies, MDPI, vol. 16(9), pages 1-22, May.
    16. Ye, Rui-Ke & Gao, Zhuang-Fei & Fang, Kai & Liu, Kang-Li & Chen, Jia-Wei, 2021. "Moving from subsidy stimulation to endogenous development: A system dynamics analysis of China's NEVs in the post-subsidy era," Technological Forecasting and Social Change, Elsevier, vol. 168(C).
    17. Meng, Jinhao & Cai, Lei & Stroe, Daniel-Ioan & Luo, Guangzhao & Sui, Xin & Teodorescu, Remus, 2019. "Lithium-ion battery state-of-health estimation in electric vehicle using optimized partial charging voltage profiles," Energy, Elsevier, vol. 185(C), pages 1054-1062.
    18. Theodoros Kalogiannis & Md Sazzad Hosen & Mohsen Akbarzadeh Sokkeh & Shovon Goutam & Joris Jaguemont & Lu Jin & Geng Qiao & Maitane Berecibar & Joeri Van Mierlo, 2019. "Comparative Study on Parameter Identification Methods for Dual-Polarization Lithium-Ion Equivalent Circuit Model," Energies, MDPI, vol. 12(21), pages 1-35, October.
    19. Izzet Alp Gul & Gülgün Kayakutlu & M. Özgür Kayalica, 2020. "Risk Analysis in Renewable Energy System (RES) Investment for a Developing Country: A Case Study in Pakistan," Arthaniti: Journal of Economic Theory and Practice, , vol. 19(2), pages 204-223, December.
    20. Correa-Florez, Carlos Adrian & Michiorri, Andrea & Kariniotakis, Georges, 2018. "Robust optimization for day-ahead market participation of smart-home aggregators," Applied Energy, Elsevier, vol. 229(C), pages 433-445.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006482. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.