Volume 2, Issue 2
Identification of a Corroded Boundary and its Robin Coefficient

B. Bin-Mohsin & D. Lesnic

East Asian J. Appl. Math.,2 (2012), pp. 126-149.

Published online: 2018-02

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  • Abstract

An inverse geometric problem for two-dimensional Helmholtz-type equations arising in corrosion detection is considered. This problem involves determining an unknown corroded portion of the boundary of a two-dimensional domain and possibly its surface heat transfer (impedance) Robin coefficient from one or two pairs of boundary Cauchy data (boundary temperature and heat flux), and is solved numerically using the meshless method of fundamental solutions. A nonlinear unconstrained minimisation of the objective function is regularised when noise is added into the input boundary data. The stability of the numerical results is investigated for several test examples, with respect to noise in the input data and various values of the regularisation parameters.

  • Keywords

Helmholtz-type equations inverse problem method of fundamental solutions regularisation

  • AMS Subject Headings

65N20 65N21 65N80

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-126, author = {B. Bin-Mohsin and D. Lesnic}, title = {Identification of a Corroded Boundary and its Robin Coefficient}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {2}, pages = {126--149}, abstract = {

An inverse geometric problem for two-dimensional Helmholtz-type equations arising in corrosion detection is considered. This problem involves determining an unknown corroded portion of the boundary of a two-dimensional domain and possibly its surface heat transfer (impedance) Robin coefficient from one or two pairs of boundary Cauchy data (boundary temperature and heat flux), and is solved numerically using the meshless method of fundamental solutions. A nonlinear unconstrained minimisation of the objective function is regularised when noise is added into the input boundary data. The stability of the numerical results is investigated for several test examples, with respect to noise in the input data and various values of the regularisation parameters.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130212.300312a}, url = {http://global-sci.org/intro/article_detail/eajam/10871.html} }
TY - JOUR T1 - Identification of a Corroded Boundary and its Robin Coefficient AU - B. Bin-Mohsin & D. Lesnic JO - East Asian Journal on Applied Mathematics VL - 2 SP - 126 EP - 149 PY - 2018 DA - 2018/02 SN - 2 DO - http://dor.org/10.4208/eajam.130212.300312a UR - https://global-sci.org/intro/article_detail/eajam/10871.html KW - Helmholtz-type equations KW - inverse problem KW - method of fundamental solutions KW - regularisation AB -

An inverse geometric problem for two-dimensional Helmholtz-type equations arising in corrosion detection is considered. This problem involves determining an unknown corroded portion of the boundary of a two-dimensional domain and possibly its surface heat transfer (impedance) Robin coefficient from one or two pairs of boundary Cauchy data (boundary temperature and heat flux), and is solved numerically using the meshless method of fundamental solutions. A nonlinear unconstrained minimisation of the objective function is regularised when noise is added into the input boundary data. The stability of the numerical results is investigated for several test examples, with respect to noise in the input data and various values of the regularisation parameters.

B. Bin-Mohsin & D. Lesnic. (1970). Identification of a Corroded Boundary and its Robin Coefficient. East Asian Journal on Applied Mathematics. 2 (2). 126-149. doi:10.4208/eajam.130212.300312a
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