IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v390y2021ics0096300320305592.html
   My bibliography  Save this article

A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography

Author

Listed:
  • Xi, Qiang
  • Fu, Zhuojia
  • Wu, Wenjie
  • Wang, Hui
  • Wang, Yong

Abstract

This paper introduces a novel localized collocation Trefftz method (LCTM) for potential-based inverse electromyography (PIE). PIE is a noninvasive technique to calculate the internal electrical potentials from measured body surface electromyographic data, which can be considered as an inverse Cauchy problem with potential equation. In the proposed LCTM, the electrical potential at every node is expressed as a linear combination of 3D Trefftz basis in each stencil support, and the sparse linear system is yield by satisfying governing equation at interior nodes and boundary conditions at boundary nodes. The proposed LCTM inherits the properties of easy-to-use and meshless from the collocation Trefftz method (CTM), and mitigates the ill-conditioning resultant matrix encountered in the CTM. Numerical efficiency of the proposed method is investigated in comparison with the CTM and experimental data.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305592
    DOI: 10.1016/j.amc.2020.125604
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320305592
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125604?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. Alves, Carlos J.S. & Valtchev, Svilen S., 2018. "On the application of the method of fundamental solutions to boundary value problems with jump discontinuities," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 61-74.
    2. Marin, Liviu & Cipu, Corina, 2017. "Non-iterative regularized MFS solution of inverse boundary value problems in linear elasticity: A numerical study," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 265-286.
    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. Bergam, A. & Chakib, A. & Nachaoui, A. & Nachaoui, M., 2019. "Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 865-878.
    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. 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. 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).
    3. Sun, Linlin & Fu, Zhuojia & Chen, Zhikang, 2023. "A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis," Applied Mathematics and Computation, Elsevier, vol. 439(C).

    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. Syrym E. Kasenov & Aigerim M. Tleulesova & Ainur E. Sarsenbayeva & Almas N. Temirbekov, 2024. "Numerical Solution of the Cauchy Problem for the Helmholtz Equation Using Nesterov’s Accelerated Method," Mathematics, MDPI, vol. 12(17), pages 1-20, August.
    2. Wang, Fajie & Zhao, Qinghai & Chen, Zengtao & Fan, Chia-Ming, 2021. "Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. 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.
    4. 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.
    5. Yancheng Li & Sina Dang & Wei Li & Yingbin Chai, 2022. "Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    6. 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.
    7. 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).
    8. Yao Sun & Shijie Hao, 2021. "A Numerical Study for the Dirichlet Problem of the Helmholtz Equation," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    9. 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.
    10. Yao Sun & Xiaoliang Wei & Zibo Zhuang & Tian Luan, 2019. "A Numerical Method for Filtering the Noise in the Heat Conduction Problem," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    11. 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.
    12. 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).
    13. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    14. 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.
    15. 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).
    16. 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.
    17. Nikan, O. & Avazzadeh, Z., 2021. "A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    18. Ellabib, Abdellatif & Nachaoui, Abdeljalil & Ousaadane, Abdessamad, 2021. "Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 231-247.

    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:390:y:2021:i:c:s0096300320305592. 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.