Geodesic
Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous Dirichlet boundary conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 27-41

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

We consider a retrospective inverse problem of heat conduction with non-stationary inhomogeneous Dirichlet boundary conditions. It is approximated by the Crank—Nicolson difference scheme, which has the second order of approximation both in the spatial variable and in time. To determine the solution of the resulting system of linear algebraic equations, it is proposed to use the iterative method of conjugate gradients. Examples are given of restoring smooth, nonsmooth, and discontinuous initial conditions, including the introduction of «noise» characteristic of additional conditions of inverse problems and its smoothing using the Savitsky—Golay filter.
Keywords: retrospective heat conductivity problem, Crank—Nicholson difference scheme, conjugate gradient method, filter Savitsky—Goley.
Mots-clés : perturbation condition 
@article{SJIM_2022_25_4_a2,
     author = {V. I. Vasil'ev and A. M. Kardashevsky and V. V. Popov},
     title = {Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous {Dirichlet} boundary conditions},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {27--41},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a2/}
}
TY  - JOUR
AU  - V. I. Vasil'ev
AU  - A. M. Kardashevsky
AU  - V. V. Popov
TI  - Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous Dirichlet boundary conditions
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2022
SP  - 27
EP  - 41
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a2/
LA  - ru
ID  - SJIM_2022_25_4_a2
ER  - 
%0 Journal Article
%A V. I. Vasil'ev
%A A. M. Kardashevsky
%A V. V. Popov
%T Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous Dirichlet boundary conditions
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2022
%P 27-41
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a2/
%G ru
%F SJIM_2022_25_4_a2
V. I. Vasil'ev; A. M. Kardashevsky; V. V. Popov. Iterative solution of a retrospective inverse problem of heat conduction with inhomogeneous Dirichlet boundary conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 4, pp. 27-41. http://geodesic.mathdoc.fr/item/SJIM_2022_25_4_a2/