Radial basis function method modelling borehole heat transfer: the practical application
In this work, the method of radial basis function (RBF) is used for the borehole heat exchanger transfers (BHET) problems. The RBF method is an efficient mesh free technique for the numerical solution of partial differential equations. The condition number of the system of linear equations (matrix...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2016-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/14936 |
| _version_ | 1818343522308194304 |
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| author | Audrius Indriulionis Pranas Vaitkus |
| author_facet | Audrius Indriulionis Pranas Vaitkus |
| author_sort | Audrius Indriulionis |
| collection | DOAJ |
| description | In this work, the method of radial basis function (RBF) is used for the borehole heat exchanger transfers (BHET) problems. The RBF method is an efficient mesh free technique for the numerical solution of partial differential equations. The condition number of the system of linear equations (matrix A) is large it means that the ill-conditioning of matrix A makes the numerical solution unstable. Tikhonov regularization (TR) method are presented to solve such ill-conditioned systems. In this work, generalized cross-validation (GCV) method is carried out to determine the regularization parameter ksi for the TR method that minimizes the GCV function. The some practical results of numerical experiments are presented. |
| first_indexed | 2024-12-13T16:31:55Z |
| format | Article |
| id | doaj.art-1191301519434a49893ad6064d809996 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-12-13T16:31:55Z |
| publishDate | 2016-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-1191301519434a49893ad6064d8099962022-12-21T23:38:29ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2016-12-0157A10.15388/LMR.A.2016.04Radial basis function method modelling borehole heat transfer: the practical applicationAudrius Indriulionis0Pranas Vaitkus1Vilnius UniversityVilnius UniversityIn this work, the method of radial basis function (RBF) is used for the borehole heat exchanger transfers (BHET) problems. The RBF method is an efficient mesh free technique for the numerical solution of partial differential equations. The condition number of the system of linear equations (matrix A) is large it means that the ill-conditioning of matrix A makes the numerical solution unstable. Tikhonov regularization (TR) method are presented to solve such ill-conditioned systems. In this work, generalized cross-validation (GCV) method is carried out to determine the regularization parameter ksi for the TR method that minimizes the GCV function. The some practical results of numerical experiments are presented.https://www.journals.vu.lt/LMR/article/view/14936borehole heat exchanger transfer (BHET)radial basis function (RBF)Tikhonov regularization (TR)generalized cross-validation (GCV) |
| spellingShingle | Audrius Indriulionis Pranas Vaitkus Radial basis function method modelling borehole heat transfer: the practical application Lietuvos Matematikos Rinkinys borehole heat exchanger transfer (BHET) radial basis function (RBF) Tikhonov regularization (TR) generalized cross-validation (GCV) |
| title | Radial basis function method modelling borehole heat transfer: the practical application |
| title_full | Radial basis function method modelling borehole heat transfer: the practical application |
| title_fullStr | Radial basis function method modelling borehole heat transfer: the practical application |
| title_full_unstemmed | Radial basis function method modelling borehole heat transfer: the practical application |
| title_short | Radial basis function method modelling borehole heat transfer: the practical application |
| title_sort | radial basis function method modelling borehole heat transfer the practical application |
| topic | borehole heat exchanger transfer (BHET) radial basis function (RBF) Tikhonov regularization (TR) generalized cross-validation (GCV) |
| url | https://www.journals.vu.lt/LMR/article/view/14936 |
| work_keys_str_mv | AT audriusindriulionis radialbasisfunctionmethodmodellingboreholeheattransferthepracticalapplication AT pranasvaitkus radialbasisfunctionmethodmodellingboreholeheattransferthepracticalapplication |