Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium

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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Main Authors: Magira Kulbay, Saule Maussumbekova, Balgaisha Mukanova
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/329052
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spelling doaj-d1fb79bac5a44a28b6a38c53b0c8e3302020-11-24T23:00:34ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Magira Kulbay
Saule Maussumbekova
Balgaisha Mukanova
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
author_facet Magira Kulbay
Saule Maussumbekova
Balgaisha Mukanova
author_sort Magira Kulbay
title 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_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_sort numerical solution of continuation problem for 3d steady-state diffusion in cylindrically layered medium
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2015-01-01
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.
url http://dx.doi.org/10.1155/2015/329052
work_keys_str_mv AT magirakulbay numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium
AT saulemaussumbekova numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium
AT balgaishamukanova numericalsolutionofcontinuationproblemfor3dsteadystatediffusionincylindricallylayeredmedium
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