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A new investigation into regularization techniques for the method of fundamental solutions

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  • Lin, Ji
  • Chen, Wen
  • Wang, Fuzhang

Abstract

This study examines different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we have investigated the relationship among the condition number, the effective condition number, and the MFS solution accuracy. Numerical results show that the damped singular value decomposition under the parameter choice of the generalized cross-validation performs the best in terms of the MFS stability analysis. We also find that the condition number is a superior criterion to the effective condition number.

Suggested Citation

  • Lin, Ji & Chen, Wen & Wang, Fuzhang, 2011. "A new investigation into regularization techniques for the method of fundamental solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1144-1152.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:6:p:1144-1152
    DOI: 10.1016/j.matcom.2010.10.030
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    Cited by:

    1. Qu, Wenzhen & Chen, Wen & Fu, Zhuojia & Gu, Yan, 2018. "Fast multipole singular boundary method for Stokes flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 57-69.
    2. Lin, Ji & Reutskiy, S.Y. & Lu, Jun, 2018. "A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 459-476.
    3. Reddy, G.M.M. & Nanda, P. & Vynnycky, M. & Cuminato, J.A., 2021. "Efficient numerical solution of boundary identification problems: MFS with adaptive stochastic optimization," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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