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A comparison of different methods to solve inverse biharmonic boundary value problems
Author(s) -
Zeb A.,
Elliott L.,
Ingham D. B.,
Lesnic D.
Publication year - 1999
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/(sici)1097-0207(19990830)45:12<1791::aid-nme654>3.0.co;2-z
Subject(s) - biharmonic equation , mathematics , boundary element method , discretization , boundary value problem , singular value decomposition , regularization (linguistics) , method of fundamental solutions , mathematical analysis , smoothing , singular boundary method , laplace's equation , inverse problem , laplace transform , finite element method , algorithm , computer science , physics , statistics , artificial intelligence , thermodynamics
The Boundary Element Method (BEM) is applied to solve numerically some inverse boundary value problems associated to the biharmonic equation which involve over‐ and under‐specified boundary portions of the solution domain. The resulting ill‐conditioned system of linear equations is solved using the regularization and the minimal energy methods, followed by a further application of the Singular Value Decomposition Method (SVD). The regularization method incorporates a smoothing effect into the least squares functional, whilst the minimal energy method is based on minimizing the energy functional for the Laplace equation subject to the linear constraints generated by the BEM discretization of the biharmonic equation. The numerical results are compared with known analytical solutions and the stability of the numerical solution is investigated by introducing noise into the input data. Copyright © 1999 John Wiley & Sons, Ltd.