TY - JOUR
T1 - Fading regularization method for an inverse boundary value problem associated with the biharmonic equation
AU - Boukraa, Mohamed Aziz
AU - Caillé, Laëtitia
AU - Delvare, Franck
N1 - Publisher Copyright:
© 2024 The Authors
PY - 2025/3/15
Y1 - 2025/3/15
N2 - In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion for the iterative process and compare its performance with previous criteria. Numerical simulations using MFS validate the accuracy of this stopping criterion for both compatible and noisy data and demonstrate the convergence, stability, and efficiency of the proposed algorithm, as well as its ability to deblur noisy data.
AB - In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion for the iterative process and compare its performance with previous criteria. Numerical simulations using MFS validate the accuracy of this stopping criterion for both compatible and noisy data and demonstrate the convergence, stability, and efficiency of the proposed algorithm, as well as its ability to deblur noisy data.
KW - Biharmonic equation
KW - Cauchy problem
KW - Inverse boundary value problems
KW - Method of fundamental solutions
UR - https://www.scopus.com/pages/publications/85204917046
U2 - 10.1016/j.cam.2024.116285
DO - 10.1016/j.cam.2024.116285
M3 - Article
AN - SCOPUS:85204917046
SN - 0377-0427
VL - 457
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 116285
ER -