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Computational Mechanics
Erschienen in: Computational Mechanics 4/2021

09.07.2021 | Original Paper

Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction

verfasst von: Andreea–Paula Voinea–Marinescu, Liviu Marin

Erschienen in: Computational Mechanics | Ausgabe 4/2021

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Abstract

The Cauchy problem in 2D and 3D steady-state anisotropic heat conduction is investigated for both exact and perturbed data, i.e. the numerical reconstruction of the missing temperature and normal heat flux on a part of the boundary from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary. This inverse Cauchy problem is solved by applying and adapting the fading regularization method, proposed by Cimetière et al.  [7, 8] for the steady-state isotropic heat conduction, to the anisotropic case. An appropriate stabilizing/regularizing stopping criterion for the resulting iterative algorithm is provided for each type of Cauchy data considered. The numerical implementation is realized for 2D and 3D homogeneous solids by using the meshless method of fundamental solutions.
Vorheriger Artikel Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes
Nächster Artikel Bayesian inversion for unified ductile phase-field fracture

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Literatur
1.
Özişik MN (1993) Heat conduction. Wiley, New York
2.
Hadamard J (1923) Lectures on Cauchy problem in linear partial differential equations. Yale University Press, New HavenMATH
3.
Dennis BH, Dulikravich GS (1999) Simultaneous determination of temperatures, heat fluxes, deformations, and tractions on inaccessible boundaries. ASME J Heat Trans 121(3):537–545CrossRef
4.
Kozlov VA, Mazya VG, Fomin AV (1991) An iterative method for solving the Cauchy problem for elliptic equations. Comput Math Math Phys 31:45–52MathSciNet
5.
Lesnic D, Elliott L, Ingham DB (1997) An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation. Eng Anal Bound Elem 20:123–133CrossRef
6.
Hào DN, Lesnic D (2000) The Cauchy problem for Laplace’s equation via the conjugate gradient method. IMA J Appl Math 65:199–217MathSciNetCrossRef
7.
Cimetière A, Delvare F, Pons F (2000) Une méthode inverse à régularisation évanescente. Comptes Rendus de l’Académie des Sciences - Série IIb - Mécanique 328:639–644MATH
8.
Cimetière A, Delvare F, Jaoua M, Pons F (2001) Solution of the Cauchy problem using iterated Tikhonov regularization. Inverse Probl 17:553–570MathSciNetCrossRef
9.
Andrieux S, Baranger TN, Ben Abda A (2005) Solving Cauchy problems by minimizing an energy-like functional. Inverse Probl 34(1):81–101MathSciNetMATH
10.
Ben Belgacem F, El Fekih H (2006) On Cauchy’s problem: I a variational Steklov-Poincare theory. Inverse Probl 21(6):1915–1936MathSciNetCrossRef
11.
Azaiez M, Ben Belgacem F, El Fekih H (2006) On Cauchy’s problem: II. Completion, regularization and approximation. Inverse Probl 22(4):1307–1336MathSciNetCrossRef
12.
Mera NS, Elliott L, Ingham DB, Lesnic D (2000) The boundary element solution for the Cauchy steady heat conduction problem in an anisotropic medium. Int J Numer Methods Eng 49:481–499CrossRef
13.
Andrieux S, Ben Abda A, Baranger TN (2005) Data completion via an energy error functional. Comptes Rendus Mecanique 333:171–177CrossRef
14.
Jin B, Zheng Y, Marin L (2006) The method of fundamental solutions for inverse boundary value problems associated with the steady-state heat conduction in anisotropic media. Int J Numer Methods Eng 65(11):1865–1891MathSciNetCrossRef
15.
Marin L (2009) An alternating iterative MFS algorithm for the Cauchy problem in two-dimensional anisotropic heat conduction. CMC Comput Mater Continua 12:71–100
16.
Marin L (2010) Stable boundary and internal data reconstruction in two-dimensional anisotropic heat conduction Cauchy problems using relaxation procedures for an iterative MFS algorithm. CMC Comput Mater Continua 17(3):233–274
17.
Hào DN, Johansson BT, Lesnic D, Hien PM (2010) A variational method and approximations of a Cauchy problem for elliptic equations. J Algorithms Comput Technol 4(1):89–119MathSciNetCrossRef
18.
Gu Y, Chen W, Zhang C, He X (2015) A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media. Int J Heat Mass Trans 84:91–102CrossRef
19.
Gu Y, Chen W, Fu Z-J (2014) Singular boundary method for inverse heat conduction problems in general anisotropic media. Inverse Probl Sci Eng 22(6):889–909MathSciNetCrossRef
20.
Marin L (2020) Landweber-Fridman algorithms for the Cauchy problem in steady-state anisotropic heat conduction. Math Mech Solids 25(6):1340–1363MathSciNetCrossRef
21.
Marin L (2020) MFS-fading regularization method for inverse BVPs in anisotropic heat conduction. In: Alves CJS, Karageorghis A, Leitão VMA, Valtchev SS (eds) Advances on Trefftz methods and their applications. Springer, Cham, Switzerland, pp 121–138CrossRef
22.
23.
Delvare F, Cimetière A, Pons F (2002) An iterative boundary element method for Cauchy inverse problems. Comput Mech 28:291–302MathSciNetCrossRef
24.
Cimetière A, Delvare F, Jaoua M, Pons F (2002) An inversion method for harmonic functions reconstruction. Int J Therm Sci 41:509–516CrossRef
25.
F. Delvare, J.L. Hanus, Complétion de données par méthode inverse en élasticité linéaire. In: 7eme Colloque National en Calcul de Structures. 17-20 May 2005, Giens, France
26.
Delvare F, Cimetière A, Hanus JL, Bailly P (2010) An iterative method for the Cauchy problem in linear elasticity with fading regularization effect. Comput Methods Appl Mech Eng 199(49–52):3336–3344MathSciNetCrossRef
27.
Marin L, Delvare F, Cimetière A (2016) Fading regularization MFS algorithm for inverse boundary value problems in two-dimensional linear elasticity. Int J Solids Struct 78–79:9–20CrossRef
28.
Caillé L, Delvare F, Marin L, Michaux-Leblond N (2017) Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Helmholtz equation. Int J Solids Struct 125:122–133CrossRef
29.
Caillé L, Marin L, Delvare F (2019) A meshless fading regularization algorithm for solving the Cauchy problem for the three-dimensional Helmholtz equation. Numer Algorithms 82(3):869–894MathSciNetCrossRef
30.
Steinbach O (2008) Numerical approximation methods for elliptic boundary value problems. Springer, New YorkCrossRef
31.
Fairweather G, Karageorghis A (1998) The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math 9:69–95MathSciNetCrossRef
Metadaten
Titel
Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction
verfasst von
Andreea–Paula Voinea–Marinescu
Liviu Marin
Publikationsdatum
09.07.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2021
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-021-02052-y

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