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Inverse stefan problem: Tracking of the interface position from measurements on the solid phase
Author(s) -
Bénard C.,
Afshari A.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350412
Subject(s) - discretization , mathematics , inverse problem , regularization (linguistics) , dimension (graph theory) , position (finance) , stefan problem , inverse , computation , minification , boundary (topology) , mathematical analysis , mathematical optimization , algorithm , computer science , geometry , finance , artificial intelligence , pure mathematics , economics
This study presents a sequential algorithm for the identification of the position s of the moving boundary of a variable one‐dimensional or two‐dimensional domain from discrete measurements, temperatures and fluxes, collected at the fixed boundary. The inverse problem is solved by minimization, with respect to s , of a penalized output least square criterion defined on a sliding time horizon of length τ. At every time step, several iterations are performed to estimate the unknown s . Each iteration consists in a guess of s , a computation of the corresponding value of the output y (direct model) and the criterion J , and a step towards a new estimation of s . The impact of the different parameters, space and time discretization intervals, regularization coefficient, dimension of the unknown parameter s , length of the observation horizon, choice of the observed output (temperature or flux) and choice of the direct model is thoroughly analysed for an analytical test case.