Geodesic
Inverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation
Filomat, Tome 34 (2020) no. 10, p. 3319

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In this paper we investigated the inverse problem of identifying an unknown time-dependent coefficient and free boundary in heat conduction equation. By using the change of variable we reduced the free boundary problem into a fixed boundary problem. In direct solver problem we employed the meshless local Petrov-Galerkin (MLPG) method based on the moving least squares (MLS) approximation. Inverse reduced problem with fixed boundary is nonlinear and we formulated it as a nonlinear least-squares minimization of a scalar objective function. Minimization is performed by using of f mincon routine from MATLAB optimization toolbox accomplished with the Interior − point algorithm. In order to deal with the time derivatives, a two-step time discretization method is used. It is shown that the proposed method is accurate and stable even under a large measurement noise through several numerical experiments.
DOI : 10.2298/FIL2010319K
Classification : 65M32, 35R35
Keywords: Inverse problem, Free boundary, Meshless local Petrov-Galerkin method, Moving least squares, Optimization 
Akbar Karami; Saeid Abbasbandy; Elyas Shivanian. Inverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation. Filomat, Tome 34 (2020) no. 10, p. 3319 . doi: 10.2298/FIL2010319K
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     author = {Akbar Karami and Saeid Abbasbandy and Elyas Shivanian},
     title = {Inverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local {Petrov-Galerkin} {(MLPG)} method via moving least squares approximation},
     journal = {Filomat},
     pages = {3319 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010319K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010319K/}
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