Identification of interface position in two-layered domain using gradient method coupled with the bem

Ewa Majchrzak¹, Bohdan Mochnacki²

¹Institute of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego 18a, 44-100 Gliwice, Poland.
²Higher School of Labour Safety Management, Bankowa 8,40-007 Katowice, Poland.

DOI:

https://doi.org/10.7494/cmms.2013.2.0440

Abstract:

The non-homogeneous domain being the composition of two sub-domains is considered, at the same time the position of internal interface is unknown. The additional information necessary to solve the identification problem results from the knowledge of temperature field at the set of points X selected from the domain analyzed. From the practical point of view the points X should be located at the external surface of the system. The steady temperature field in domain considered is described by two energy equations (the Laplace equations), continuity condition given on the contact surface and the boundary conditions given on the external surface of domain. To solve the inverse problem the gradient method is used. The sensitivity coefficients appearing in the final form of equation which allows one to find the solution using a certain iterative procedure are determined by means of the implicit approach of shape sensitivity analysis. This approach is especially convenient in the case of boundary element method application (this method is used at the stage of numerical algorithm construction). In the final part of the paper the examples of computations are shown.

Cite as:

Majchrzak, E., & Mochnacki, B. (2013). Identification of interface position in two-layered domain using gradient method coupled with the bem. Computer Methods in Materials Science, 13(2), 264-268. https://doi.org/10.7494/cmms.2013.2.0440

Article (PDF):

Keywords:

Heat transfer, Inverse problem, Gradient method, Boundary element method

References:

Brebbia, C.A., Dominguez J., 1992, Boundary elements, an introductory course. CMP, McGraw-Hill Book Company, London.

Burczyński, T., 2003, Sensitivity analysis, optimization and inverse problems, Boundary element advances in solid mechanics, eds, Beskos, D., Maier, G., Springer Verlag, Vien, New York, 245-307.

Ciesielski, M., Mochnacki, B., 2012, Numerical analysis of interactions between skin surface temperature and burn wound shape, Scientific Research of Institute of Mathematics and Computer Science, 1, 15-22.

Freus, S., Freus, K., Majchrzak, E., Mochnacki, B., 2012, Identification of internal boundary position in two-layers domain on the basis of external surface temperature distribution, CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), eds, Eberhardsteiner, J., Bohm, H.J., Rammerstorfer, F.G., Vienna University of Technology, Vienna, Austria,

Kleiber, M., Parameter sensitivity, 1997, J.Wiley & Sons Ltd., Chichester.

Kurpisz, K., Nowak, A.J. Inverse Thermal Problems, 1995, Computational Mechanics Publications, Southampton-Boston.

Romero Mendez, R., Jimenez-Lozano, J.N., Sen, M., Gonzalez, F.J., 2010, Analytical solution of a Pennes equation for burn-depth determination from infrared thermographs, Mathematical Medicine and Biology, 27, 21-38.

Majchrzak, E., 2001,Boundary element method in heat transfer, Publ. of the Czestochowa University of Technology, Czestochowa (in Polish).

Majchrzak, E., Freus, K., Freus, S., 2011, Shape sensitivity analysis. Implicit approach using boundary element method, Scientific Research of the Institute of Mathematics and Computer Science, 1, 151-162.