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Conjugate gradient method for the Robin inverse problem associated with the Laplace equation
Author(s) -
Jin Bangti
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1949
Subject(s) - conjugate gradient method , inverse problem , mathematics , laplace's equation , laplace transform , convergence (economics) , boundary (topology) , benchmark (surveying) , nonlinear conjugate gradient method , computation , finite element method , boundary value problem , mathematical optimization , mathematical analysis , algorithm , computer science , gradient descent , artificial neural network , physics , geodesy , machine learning , geography , economics , thermodynamics , economic growth
This paper studies a non‐linear inverse problem associated with the Laplace equation of identifying the Robin coefficient from boundary measurements. A variational formulation of the problem is suggested, thereby transforming it into an optimization problem. Mathematical properties relevant to its numerical computation are established. The optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle, and the algorithm is implemented using the boundary element method. Numerical results are presented for several benchmark problems with both exact and noisy data, and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated. Copyright © 2006 John Wiley & Sons, Ltd.