Application of Meshless Methods for Solving an Inverse Heat Conduction Problem

Alimardan Shahrezaee, Malihe Rostamian

Abstract

In this paper, we consider the inverse problem of determining the unknown temperature
at x = 0 and section of initial condition at t = 0 in an inverse heat conduction problem (IHCP).
Two new numerical methods are developed by using the solution of an auxiliary problem and
heat polynomials as basis functions in presence of noisy data. Due to ill-posed IHCP, we use
the Tikhonov regularization technique with the GCV scheme to solve the resulting matrix system
of the basis function methods (BFM). Some numerical examples are presented to illustrate the
strength of the methods.

Keywords

IHCP; Basis function method; Tikhonov regularization method; meshless method; GCV; Ill-conditioned; Heat polynomials; Auxiliary problem.

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