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Journal Paper

A New Approximate Method for an Inverse Time-Dependent Heat Source Problem Using Fundamental Solutions and RBFs

Engineering Analysis with Boundary Elements, Vol. 64, (2016) 278-289.

This paper presents a meshless numerical scheme to solve the inverse heat source time dependent problem. Fundamental solutions of heat equations and radial basis functions (RBFs) are used to obtain a numerical solution. Since the coefficient matrix may be ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulting system of linear equations. Therefore, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. The accuracy and efficiency of the proposed method is illustrated by some numerical examples.

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Categories
Journal Paper

A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

Advances in Mathematical Physics, Vol. 2015, Article ID 256726, 8 pages

We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.

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@Copyright 2020  Dr. Amirfakhrian  | Powered by Applied Plan