- Tytuł:
- Solution of inverse heat conduction equation with the use of Chebyshev polynomials
- Autorzy:
-
Joachimiak, M.
Frąckowiak, A.
Ciałkowski, M. - Powiązania:
- https://bibliotekanauki.pl/articles/239926.pdf
- Data publikacji:
- 2016
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
Laplace’s equation
boundary inverse problem
quasi-Cauchy problem
stability of the inverse problem
równanie Laplace'a
brzegowe zagadnienie odwrotne
Problem Quasi-Cauchy'ego - Opis:
- A direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.
- Źródło:
-
Archives of Thermodynamics; 2016, 37, 4; 73-88
1231-0956
2083-6023 - Pojawia się w:
- Archives of Thermodynamics
- Dostawca treści:
- Biblioteka Nauki
Artykuł