Geodesic
Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 393-408 
A. V. Penenko. Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 393-408. http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a4/
@article{SJVM_2012_15_4_a4,
     author = {A. V. Penenko},
     title = {Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a~layered medium with gradient methods},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {393--408},
     year = {2012},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a4/}
}
TY  - JOUR
AU  - A. V. Penenko
TI  - Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2012
SP  - 393
EP  - 408
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a4/
LA  - ru
ID  - SJVM_2012_15_4_a4
ER  - 
%0 Journal Article
%A A. V. Penenko
%T Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2012
%P 393-408
%V 15
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a4/
%G ru
%F SJVM_2012_15_4_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

A method for constructing numerical schemes for inverse coefficient inverse heatconduction problem with boundary measurement data and piecewise-constant coefficients is considered. A set of numerical schemes for a gradient optimization algorithm is presented. The method is based on the combined use of locally-adjoint problems along with approximation methods in the Hilbert spaces.

[1] Penenko V. V., Metody chislennogo modelirovaniya atmosfernykh protsessov, Gidrometizdat, Leningrad, 1981 | MR

[2] Karchevskii A .L., “Korrektnaya skhema deistvii pri chislennom reshenii obratnoi zadachi optimizatsionnym metodom”, Sib. zhurn. vychisl. matematiki (RAN. Sib. otd-nie, Novosibirsk), 11:2 (2008), 139–149

[3] Samarskii A. A., Vabischevich P. N., Vychislitelnaya teploperedacha, LKI, M., 2007

[4] Godunov S. K., Ryabenkii V. S., Raznostnye skhemy: vvedenie v teoriyu, Nauka, M., 1977 | MR

[5] Marchuk G. I., Metody vychislitelnoi matematiki, Lan, M., 2009

[6] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[7] Streng G., Fiks D., Teoriya metoda konechnykh elementov, Mir, M., 1984

[8] Infield L., Hull T., “The factorization method”, Reviews of Modern Physics, 23:1 (1951), 21–68 | DOI | MR

[9] El-Mistikawy T. M., Werle M. J., “Numerical method for boundary layers with blowing. The exponential box scheme”, AIAA J., 16 (1978), 749–751 | DOI | Zbl

[10] Berger A. E., Solomon J. M., Ciment M., “An analysis of a uniformly accurate difference method for a singular perturbation problem”, Mathematics of computation, 37:155 (1981), 79–94 | DOI | MR | Zbl

[11] Korneev V. G., “O tochnykh setochnykh skhemakh”, Zhurn. vychisl. matematiki i mat. fiziki, 22:3 (1982), 646–654 | MR | Zbl

[12] Zverev V. G., Goldin V. D., “Raznostnaya skhema dlya resheniya kovektivno-diffuzionnykh zadach teplomassoperenosa”, Vychislitelnye tekhnologii, 7:6 (2002), 24–37 | MR | Zbl

[13] Voevodin A. F., “Metod faktorizatsii dlya lineinykh i kvazilineinykh singulyarno vozmuschennykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii”, Sib. zhurn. vychisl. matematiki (RAN. Sib. otd-nie, Novosibirsk), 12:1 (2009), 1–15 | Zbl

[14] Penenko V. V., Tsvetova E. A., “Discrete-analytical methods for the implementation of variational principles in environmental applications”, J. of Computational and Applied Mathematics, 226 (2009), 319–330 | DOI | MR | Zbl

[15] Hasanov A., DuChateau P., Pektas B., “An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation”, J. of Inverse and Ill-Posed Problems, 14:4 (2006), 1–29 | MR

[16] Penenko V. V., Nekotorye problemy vychislitelnoi i prikladnoi matematiki, ed. M. M. Lavrentev, Nauka, Novosibirsk, 1975, 61–77 | MR

[17] Polak E., Chislennye metody optimizatsii, Mir, M., 1974 | MR | Zbl