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Solution of a multidimensional inverse radiation problem by means of mode reduction
Author(s) -
Park H. M.,
Sung M. C.
Publication year - 2004
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.1028
Subject(s) - galerkin method , inverse problem , inverse , reduction (mathematics) , mathematics , computation , conjugate gradient method , thermal conduction , radiation , minification , mathematical analysis , mathematical optimization , physics , finite element method , algorithm , optics , geometry , thermodynamics
The Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.