SemiAnalytical Solution to Heat Transfer Problems Using Fourier Transform Technique, Radial Basis Functions, and the Method of Fundamental Solutions

Abstract

An analytically based approach for solving a transient heat transfer equation in a bounded two dimensional domain is proposed. The major features of the method are time-Fourier transformation of the problem, analytical derivation of an elementary particular solution for a localized radial basis δ-like source using the space-Fourier transform, expansion of the total particular solution in terms of those elementary particular solutions, approximation of the homogeneous solution using the method of fundamental solution, and inversion into the time domain using fast Fourier transform. The prime distinction of this scheme from the closest analogs lies in the construction of the particular solution.

The work is supported by NATO Collaborative Linkage Grant PST.CLG.980398 and by the Russian Foundation for Basic Research (Grant 04-01-00801). The authors also thank Prof. Barry Piazza for proofreading the article.