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An inverse problem in estimating the relaxation time for nanoscale phonon radiative transfer problem
Author(s) -
Huang ChengHung,
Chen KuanYu,
Kim Sin
Publication year - 2007
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.1989
Subject(s) - conjugate gradient method , relaxation (psychology) , phonon , inverse problem , radiative transfer , inverse , nanoscopic scale , physics , differential equation , differential (mechanical device) , statistical physics , mathematics , mathematical analysis , mathematical optimization , optics , condensed matter physics , quantum mechanics , geometry , thermodynamics , psychology , social psychology
An inverse nanoscale phonon radiative transfer problem is solved in this study by using conjugate gradient method (CGM) to estimate the unknown frequency‐ and temperature‐dependent relaxation time, based on the simulated phonon intensity measurements. The CGM in dealing with the present integro‐differential governing equations is not as straightforward as for the normal differential equations; special treatments are needed to overcome the difficulties. Results obtained in this inverse analysis will be justified based on the numerical experiments where two different unknown distributions of relaxation time are to be estimated. Finally, it is shown that the reliable frequency and temperature‐dependent relaxation time can be obtained with CGM. Copyright © 2007 John Wiley & Sons, Ltd.