<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the biharmonic equation. It consists to complete the missing data on the inaccessible part from the measured data on the accessible part of the boundary. To solve this ill-posed problem, we opted for the alternative iterative method developed by Kozlov, Mazya and Fomin which is a convergent method for the elliptical Cauchy problems in general. The numerical implementation of the iterative algorithm is based on the application of the boundary element method (BEM) for a sequence of mixed well-posed direct problems. Numerical results are performed for a square domain showing the effectiveness of the algorithm by BEM to produce accurate and stable numerical results.</p></abstract>

In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the biharmonic equation. It consists to complete the missing data on the inaccessible part from the measured data on the accessible part of the boundary. To solve this ill-posed problem, we opted for the alternative iterative method developed by Kozlov, Mazya and Fomin which is a convergent method for the elliptical Cauchy problems in general. The numerical implementation of the iterative algorithm is based on the application of the boundary element method (BEM) for a sequence of mixed well-posed direct problems. Numerical results are performed for a square domain showing the effectiveness of the algorithm by BEM to produce accurate and stable numerical results.

Iterative Method to Solve a Data Completion Problem for Biharmonic Equation for Rectangular Domain

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this work, we are interested in a class of problems of great importance in many areas of industry and engineering. It is the invese problem for the...

Iterative Method to Solve a Data Completion Problem for Biharmonic Equation for Rectangular Domain

Published Online: Sep 02, 2017

Page range: 129 - 147

Received: Jul 11, 2016

Accepted: Apr 01, 2017

DOI: https://doi.org/10.1515/awutm-2017-0010

Keywords
inverse problem, biharmonic equation, iterative method, boundary element method

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Iterative Method to Solve a Data Completion Problem for Biharmonic Equation for Rectangular Domain

Published Online: Sep 02, 2017

Page range: 129 - 147

Received: Jul 11, 2016

Accepted: Apr 01, 2017

DOI: https://doi.org/10.1515/awutm-2017-0010

Keywordsinverse problem, biharmonic equation, iterative method, boundary element method

© Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
inverse problem, biharmonic equation, iterative method, boundary element method