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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/256726 |
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| _version_ | 1849683972475322368 |
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| author | Muhammad Arghand Majid Amirfakhrian |
| author_facet | Muhammad Arghand Majid Amirfakhrian |
| author_sort | Muhammad Arghand |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-cbe275fccfd04eefaed33feb1ad3f781 |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-cbe275fccfd04eefaed33feb1ad3f7812025-08-20T03:23:37ZengWileyAdvances 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2015/256726 |
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