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A numerical method for the solution of two‐dimensional inverse heat conduction problems
Author(s) -
Reinhardt H.J.
Publication year - 1991
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.1620320209
Subject(s) - thermal conduction , mathematics , inverse problem , heat equation , mathematical analysis , numerical analysis , partial differential equation , inverse , elliptic partial differential equation , geometry , physics , thermodynamics
A numerical method for the solution of inverse heat conduction problems in two‐dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's 8 method to two spatial dimensions and also utilizes future times in order to stabilize the ill‐posedness of the underlying problems. The approach relies on a line approximation of the elliptic part of the parabolic differential equation leading to a system of one‐dimensional problems which can be decoupled.