Fast solution of inverse heat transfer problems by general ray method and applications to modeling of nanostructured materials

Аuthors

Alifanov O. M.^1*, Grebennikov A. I.^2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Autonomous University of Puebla, C.P. Puebla, 72570, MÉXICO

*e-mail: o.alifanov@yandex.ru
**e-mail: agrebe@fcfm.buap.mx

Abstract

We consider mathematical statement of the inverse heat conduction problem as inverse coefficient problem for linear parabolic equation. New General Ray (GR) method for solution of this problem is proposed. The method is based on reduction of Partial Differential Equation (PDE) to assemblage of Ordinary Differential Equations using local traces for considered functions and operators. GR-method presents the solution of the inverse problem for this type of equations by explicit analytical formulas that use the direct and inverse Radon transforms. Proposed version of GR-method can be realized as algorithms and computer software faster as all known ones, based on traditional approaches. This is very important for mathematical simulation at the developing ofnanostructured materials with special heat-conductive properties. 

Keywords:

coefficient inverse problem for PDE, General Ray method, regularization