Trefftz numerical functions for solving inverse heat conduction problems
[ 1 ] Instytut Energetyki Cieplnej, Wydział Inżynierii Środowiska i Energetyki, Politechnika Poznańska | [ P ] employee
2022
scientific article
english
- Inverse heat conduction problem
- Trefftz function
- Tikhonov regularization
- Conjugate gradient
EN This paper presents a concept of solving the inverse heat conduction problem with the use of a linear combination of functions satisfying the differential equation in terms of identity, that is Trefftz functions. Characteristic feature of Trefftz functions applied for solving the heat equation is lack of their analytical form. It is known that these functions satisfy the differential equation with known boundary conditions. It was proved that so defined Trefftz functions create a complete system of functions to develop the solution to the heat conduction equation. It means that solving the inverse problem is reduced to determining unknown coefficients of the linear combination of basis functions, obtained from the solution of the direct problem. Two examples of inverse problems were solved: using the conjugate gradient method and using the Tikhonov regularization. As the first example, the inverse heat conduction problem was solved in the rectangle domain with known analytical solution to this problem and with verified stability of this solution. The second example concerns determination of temperature distribution on internal boundaries of the multiply-connected domain for the material, the heat conduction coefficient of which is the function of temperature.
107566-1 - 107566-9
article number: 107566
140
4,5