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

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

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...

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Main Authors: Muhammad Arghand, Majid Amirfakhrian
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/256726
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spelling doaj-cbe275fccfd04eefaed33feb1ad3f7812021-07-02T06:16:29ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/256726256726A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction ProblemMuhammad Arghand0Majid Amirfakhrian1Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IranDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IranWe 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.http://dx.doi.org/10.1155/2015/256726
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Arghand
Majid Amirfakhrian
spellingShingle Muhammad Arghand
Majid Amirfakhrian
A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
Advances in Mathematical Physics
author_facet Muhammad Arghand
Majid Amirfakhrian
author_sort Muhammad Arghand
title A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
title_short A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
title_full A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
title_fullStr A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
title_full_unstemmed A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem
title_sort meshless method based on the fundamental solution and radial basis function for solving an inverse heat conduction problem
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/256726
work_keys_str_mv AT muhammadarghand ameshlessmethodbasedonthefundamentalsolutionandradialbasisfunctionforsolvinganinverseheatconductionproblem
AT majidamirfakhrian ameshlessmethodbasedonthefundamentalsolutionandradialbasisfunctionforsolvinganinverseheatconductionproblem
AT muhammadarghand meshlessmethodbasedonthefundamentalsolutionandradialbasisfunctionforsolvinganinverseheatconductionproblem
AT majidamirfakhrian meshlessmethodbasedonthefundamentalsolutionandradialbasisfunctionforsolvinganinverseheatconductionproblem
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