Moving Heat Source Reconstruction from Cauchy Boundary Data : The Cartesian Coordinates Case
Joint Authors
Roberty, Nilson C.
Rainha, Marcelo L. S.
de Sousa, Denis M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-24
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain.
By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha (2010a), we can treat the problem with methods similar to that used in the analysis of the stationary source reconstruction problem.
Further, the finite difference θ-scheme applied to the transient heat conduction equation leads to a model based on a sequence of modified Helmholtz equation solutions.
For each modified Helmholtz equation the characteristic interval and parallelepiped source function may be reconstructed uniquely from the Cauchy boundary data.
Using representation formula we establish reciprocity functional mapping functions that are solutions of the modified Helmholtz equation to their integral in the unknown characteristic support.
Numerical experiment for capture of an interval and an rectangular parallelepiped characteristic source inside a cubic box domain from boundary data are presented in threedimensional and one-dimensional implementations.
The problem of centroid determination is addressed and questions are discussed from an computational points of view.
American Psychological Association (APA)
Roberty, Nilson C.& de Sousa, Denis M.& Rainha, Marcelo L. S.. 2011. Moving Heat Source Reconstruction from Cauchy Boundary Data : The Cartesian Coordinates Case. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-19.
https://search.emarefa.net/detail/BIM-448130
Modern Language Association (MLA)
Roberty, Nilson C.…[et al.]. Moving Heat Source Reconstruction from Cauchy Boundary Data : The Cartesian Coordinates Case. Mathematical Problems in Engineering No. 2011 (2011), pp.1-19.
https://search.emarefa.net/detail/BIM-448130
American Medical Association (AMA)
Roberty, Nilson C.& de Sousa, Denis M.& Rainha, Marcelo L. S.. Moving Heat Source Reconstruction from Cauchy Boundary Data : The Cartesian Coordinates Case. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-19.
https://search.emarefa.net/detail/BIM-448130
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-448130