Trefftz method for an inverse geometry problem in steady-state heat conduction

• Autorzy: Hożejowski L.

Identyfikatory

DOI

10.17512/jamcm.2016.2.05

• Języki publikacji: EN

Abstrakty

EN

The paper addresses a boundary identification problem in two-dimensional steady-state heat conduction. The proposed approach based on the Trefftz method allows one to reconstruct the unknown part of a regular domain boundary from the given temperature measurements on it, provided that both the temperature and heat flux on the remaining part of the boundary are known. The reconstruction of an unknown boundary is done through successive approximations with a polynomial or a truncated Fourier series. The proposed solution method, whose merit lies in the avoidance of large systems of nonlinear equations, is fast converging, accurate and numerically stable, as demonstrated in the included numerical examples.

Słowa kluczowe

EN

inverse geometry problem; boundary identification; Trefftz method

PL

metoda Trefftza

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 2
• Strony: 41--52
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Hożejowski L.

• Department of Computer Science and Applied Mathematics, Kielce University of Technology Kielce, Poland

Bibliografia

• [1] Marin L., Karageorghis A., Regularized MFS-based boundary identification in two-dimensional Helmholtz-type equation, CMC: Computers, Materials & Continua 2008, 10, 3, 259-293.
• [2] Gonzalez M., Goldschmit M., Inverse geometry heat transfer problem based on radial basis functions geometry representation, International Journal for Numerical Methods in Engineering 2006, 65, 8, 1243-1268.
• [3] Lesnic D., Berger J.R., Martin P.A., A boundary element regularization method for the boundary determination in potential corrosion damage, Inverse Problems in Engineering 2002, 10, 2, 163-182
• [4] Kazemzadeh-Parsi M.J., Daneshmand F., Solution of geometric inverse conduction problems by smoothed fixed grid finite element method, Finite Elements in Analysis and Design 2009, 45, 599-611.
• [5] Burger M., A framework for the construction of level set methods for shape optimization and reconstruction, Interfaces and Free Boundaries 2003, 5, 301-329.
• [6] Fan C.-M., Chan H.-F., Modified collocation Trefftz method for the geometry boundary identification problem of heat conduction, Numerical Heat Transfer, Part B 2011, 59, 58-75.
• [7] Fan C.-M., Chan H.-F., Kuo C.-L., Yeih W., Numerical solutions of boundary detection problems using modified collocation Trefftz method and exponentially convergent scalar homotopy algorithm, Engineering Analysis with Boundary Elements 2012, 36, 2-8.
• [8] Chan H.-F., Fan C.-M., The modified collocation Trefftz method and exponentially convergent scalar homotopy algorithm for the inverse boundary determination problem for the biharmonic equation, Journal of Mechanics 2013, 29, 02, 363-372.
• [9] Fan C.-M., Liu Y.-C., Chan H.-F., Hsiao S.-S., Solutions of boundary detection problems for modified Helmholz equation by Trefftz method, Inverse Problems in Science and Engineering 2014, 22, 2, 267-281.
• [10] Karageorghis A., Lesnic D., Marin L., Regularized collocation Trefftz method for void detection in two-dimensional steady-state heat conduction problems, Inverse Problems in Science and Engineering 2014, 22, 3, 395-418.
• [11] Marin L., Karageorghis A., Lesnic D., The MFS for numerical boundary identification in two-dimensional harmonic problems, Engineering Analysis with Boundary Elements 2011, 35, 342-354.
• [12] Karageorghis A., Lesnic D., Marin L., The MFS for inverse geometric problems, [in:] Inverse Problems and Computational Mechanics, eds. L. Marin, L. Munteanu, V. Chiroiu, Editura Academiei Române, Bucharest 2011.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.