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

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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
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    References listed on IDEAS

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    1. 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.
    2. 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).
    3. 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.
    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.
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    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).

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