Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium
This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the ou...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/329052 |
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| _version_ | 1850174102832152576 |
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| author | Magira Kulbay Saule Maussumbekova Balgaisha Mukanova |
| author_facet | Magira Kulbay Saule Maussumbekova Balgaisha Mukanova |
| author_sort | Magira Kulbay |
| collection | DOAJ |
| description | This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data. |
| format | Article |
| id | doaj-art-d1fb79bac5a44a28b6a38c53b0c8e330 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1fb79bac5a44a28b6a38c53b0c8e3302025-08-20T02:19:43ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/329052329052Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered MediumMagira Kulbay0Saule Maussumbekova1Balgaisha Mukanova2Department of Mathematical and Computing Modelling, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanDepartment of Mathematical and Computing Modelling, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanFaculty of Mathematics and Mechanics, L.N.Gumilyov Eurasian National University, Astana 010008, KazakhstanThis work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data.http://dx.doi.org/10.1155/2015/329052 |
| spellingShingle | Magira Kulbay Saule Maussumbekova Balgaisha Mukanova Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium Abstract and Applied Analysis |
| title | Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium |
| title_full | Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium |
| title_fullStr | Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium |
| title_full_unstemmed | Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium |
| title_short | Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium |
| title_sort | numerical solution of continuation problem for 3d steady state diffusion in cylindrically layered medium |
| url | http://dx.doi.org/10.1155/2015/329052 |
| work_keys_str_mv | AT magirakulbay numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium AT saulemaussumbekova numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium AT balgaishamukanova numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium |