Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling
This work deals with a question in the mathematical modelling for the temperature evolution in a bar, for a long time linked as an inverse problem. The onedimensional model is the parabolic partial differential equation ut = α uxx, known as the heat diffusion equation. The classic direct problem (DP...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Graz University of Technology
2020-09-01
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| Series: | Journal of Universal Computer Science |
| Subjects: | |
| Online Access: | https://lib.jucs.org/article/24112/download/pdf/ |
| _version_ | 1819067720261435392 |
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| author | Augusto C. de Castro Barbosa Carlos De Moura Jhoab De Negreiros J. Mesquita de Souza Aguiar |
| author_facet | Augusto C. de Castro Barbosa Carlos De Moura Jhoab De Negreiros J. Mesquita de Souza Aguiar |
| author_sort | Augusto C. de Castro Barbosa |
| collection | DOAJ |
| description | This work deals with a question in the mathematical modelling for the temperature evolution in a bar, for a long time linked as an inverse problem. The onedimensional model is the parabolic partial differential equation ut = α uxx, known as the heat diffusion equation. The classic direct problem (DP) involves this equation coupled to a set of constraints: initial and boundary conditions, in such a way as to guarantee existence of a unique solution. The data completion (DC) problem hereby considered may be described as follows: the temperature at one of the bar extreme points is unknown but there is a fixed interior point where it may be measured, for all time. Finite difference algorithms (FDA) were tested to approximate the solution for such a problem. The important point to be emphasized is that FDA may show up distinct performances when applied to either DP or DC, which is due to the way the discrete variables follow up the mesh steps - advancing in time, for the first case, on the space direction, for the other. |
| first_indexed | 2024-12-21T16:22:44Z |
| format | Article |
| id | doaj.art-ba07c97045f9414b9e1b87bc2513d9ce |
| institution | Directory Open Access Journal |
| issn | 0948-6968 |
| language | English |
| last_indexed | 2024-12-21T16:22:44Z |
| publishDate | 2020-09-01 |
| publisher | Graz University of Technology |
| record_format | Article |
| series | Journal of Universal Computer Science |
| spelling | doaj.art-ba07c97045f9414b9e1b87bc2513d9ce2022-12-21T18:57:32ZengGraz University of TechnologyJournal of Universal Computer Science0948-69682020-09-012691177118810.3897/jucs.2020.06124112Numerical Treatment of a Data Completion Problem in Heat Conduction ModellingAugusto C. de Castro Barbosa0Carlos De Moura1Jhoab De Negreiros2J. Mesquita de Souza Aguiar3UERJ - Rio de Janeiro State UniversityUERJ - Rio de Janeiro State UniversityUNIGRANRIO - Great Rio UniversityUERJ - Rio de Janeiro State UniversityThis work deals with a question in the mathematical modelling for the temperature evolution in a bar, for a long time linked as an inverse problem. The onedimensional model is the parabolic partial differential equation ut = α uxx, known as the heat diffusion equation. The classic direct problem (DP) involves this equation coupled to a set of constraints: initial and boundary conditions, in such a way as to guarantee existence of a unique solution. The data completion (DC) problem hereby considered may be described as follows: the temperature at one of the bar extreme points is unknown but there is a fixed interior point where it may be measured, for all time. Finite difference algorithms (FDA) were tested to approximate the solution for such a problem. The important point to be emphasized is that FDA may show up distinct performances when applied to either DP or DC, which is due to the way the discrete variables follow up the mesh steps - advancing in time, for the first case, on the space direction, for the other.https://lib.jucs.org/article/24112/download/pdf/inverse problemdata completiondiffusion equati |
| spellingShingle | Augusto C. de Castro Barbosa Carlos De Moura Jhoab De Negreiros J. Mesquita de Souza Aguiar Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling Journal of Universal Computer Science inverse problem data completion diffusion equati |
| title | Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling |
| title_full | Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling |
| title_fullStr | Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling |
| title_full_unstemmed | Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling |
| title_short | Numerical Treatment of a Data Completion Problem in Heat Conduction Modelling |
| title_sort | numerical treatment of a data completion problem in heat conduction modelling |
| topic | inverse problem data completion diffusion equati |
| url | https://lib.jucs.org/article/24112/download/pdf/ |
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