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1
Content available remote Determination of surface location between two sub-domains using the temperature distribution on the external surface
100%
Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
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tom Vol. 11, nr 4
35-42
EN
In the paper two sub-domains which are in thermal contact are considered. The temperature field in these domains is described by the system of two Laplace equations supplemented by the boundary conditions. The position of surface between sub-domains is unknown. Additional information necessary to solve the identification problem results from a knowledge of external surface temperature distribution. The direct problem is solved using the boundary element method. To solve the inverse problem formulated the gradient method is applied. In the final part of the paper the results of computations are shown. The algorithm proposed here can be used, among others, in the medical practice (e.g. in burns therapy).
2
Content available remote Identification of boundary heat flux using the sensitivity coefficients
100%
Majchrzak E. , Freus K.
Archiwum Odlewnictwa
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2001
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tom R. 1, nr 2
238--243
EN
In the paper the method of boundary heat flux identification is presented. The algorithm is constructed on the basis of the least squares criterion in which the sensitivity coefficients are introduced. The method can be useful for the analysis of continuous casting technology. In the final part the example of computations is shown.
PL
W pracy przedstawiono metodę identyfikacji brzegowego strumienia ciepła na fragmencie brzegu ograniczającego analizowany obszar ciała stałego. Może być to np. krystalizator urządzenia COS pracującego w warunkach pseudoustalonego przepływu ciepła. Algorytm skonstruowano na podstawie kryterium najmniejszych kwadratów, w którym wykorzystano współczynniki wrażliwości. Jak wspomniano, metoda może być użyteczna przy analizie technologii odlewania ciągłego. W końcowej części pracy pokazano przykład obliczeń numerycznych.
3
Identification of heat flux on the contact surface of the continous casting mould
100%
Majchrzak E. , Freus K.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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1998
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tom z. 57
13-16
4
Content available remote Reconstruction of boundary condition on the internal surface of continuous casting mould
100%
Majchrzak E. , Freus K.
Krzepnięcie Metali i Stopów
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2000
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tom R. 2, nr 44
211--216
EN
In the paper the method of identification of heat flux on the contact surface between the cast slab and continuous casting mould is presented. The algorithm is constructed using the boundary element method supplemented by the least squares criterion. In the final part the example of computations is shown.
PL
W pracy przedstawiono metodę identyfikacji strumienia ciepła wymienianego między wlewkiem ciągłym a krystalizatorem urządzenia COS. Algorytm zbudowano wykorzystując metodę elementów brzegowych oraz kryterium najmniejszych kwadratów.
5
Application of nurbs curves in numerical modelling of heat transfer using the BEM
100%
Majchrzak E. , Freus K.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2009
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tom z. 95
83-84
6
Content available Algorithm of rebuilding a boundary of domain during creation of an optimal shape
100%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2016
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tom Vol. 15, nr 1
17--24
EN
In order to achieve the desired topology we often have to remove material of the area considered. This work presents the author's algorithm which can be used in the reconstruction of the boundary of domain after elimination of a certain amount of material. The paper introduces some details about the procedure that allows one to achieve the expected shape of a domain. The topological-shape sensitivity method for the Laplace equation is used to obtain an optimal topology, whereas numerical methodology utilizes the boundary element method. In the conclusion of the paper the example of computation is shown.
7
Application of sensitivity analysis to the identification of the Neumann condition
100%
Majchrzak E. , Freus K.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2001
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tom Vol. 279, z. 72
201-204
8
Content available Determination of an optimal shape of domain using the topological derivative and the Boundary Element Method
100%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2014
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tom Vol. 13, nr 4
41--48
EN
In the paper, the topological derivative for the Laplace equation is taken into account. The governing equation is solved by means of the Boundary Element Method. The topological-shape sensitivity method is used to determine the points showing the lowest sensitivities. On the selected points, material is eliminated by opening a hole, using the appropriate iterative process. This one is halted when a given amount of material is removed. The objective of this work is to obtain an optimal topology of the domain considered. In the final part of the paper, the example of computations is shown.
9
Content available remote Boundary element method in the inverse problems of steady heat transfer
100%
Majchrzak E. , Freus K.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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tom Vol. 2, nr 1
77--86
EN
The methods of inverse problems solution appearing in the domain of steady heat transfer are discussed. In particular, the inverse boundary problems (the identification of the boundary values on the part of the surface limiting the system analyzed) and the inverse parametric problems (reconstruction of the thermophysical parameters of the material) are considered. Such problems have been solved using (on the stage of numerical computations) the boundary element method. The different methods of inverse problems solution have been applied. So, the direct method, the least squares method in the basic version, the same method supplemented by the regularization terms, the method of the energy minimization and also the algorithm basing on the sensitivity coefficients have been taken into account. The computations can been realized for different numbers and positions of the control points, the possible disturbances of 'measured' temperatures have been also taken into account. The remarks concerning the exactness and effectiveness of successive methods of the inverse problem solution have been formulated. The theoretical considerations are supplemented by the examples of computations verifying the correctness of the algorithms proposed. by the examples of computations verifying the correctness of the algorithms proposed.
10
Content available remote Determination of temperature field in domain of complex shape using the NURBS curves and BEM
100%
Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2008
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tom Vol. 7, nr 1
43-48
11
Content available Applying the topological derivative and the boundary element method to design of shape of the heat exchanger
100%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2015
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tom Vol. 14, nr 2
5--12
EN
In this work, the topological derivative for the Laplace equation is used to solve a design problem. This derivative describes the sensitivity of the problem when a small hole is formed at an arbitrary point of the domain. The goal of this work is to design topology of the domain when the Robin condition is imposed on the holes. Physically, the holes can be construed as cooling channels. For finding the solution of the governing equation the boundary element method is applied. The final part of the paper presents the design of the heat exchanger and results of computations.
12
Content available remote Estimation of temperature changes due to perturbation of local geometry of boundary using implicit approach of shape sensitivity analysis
100%
Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2011
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tom Vol. 10, nr 2
65-73
EN
In the paper, a 2D domain in which the temperature field is described by the Laplace equation and the assumed boundary conditions is considered. To estimate the changes of temperature due to the change of the boundary local geometry, the implicit approach of shape sensitivity analysis is used. In the final part of paper, examples of numerical computations are shown and conclusions are formulated.
13
Content available remote Shape sensitivity analysis of temperature distribution in a non-homogeneous domain
100%
Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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tom Vol. 11, nr 2
33-41
EN
The heated non-homogeneous domain from the two sub-domains compound is considered. The temperature distribution is described by the system of two Laplace equations. At the surface Γ c between sub-domains the ideal contact is assumed, at the remaining surfaces the Dirichlet, Neumann and Robin conditions are taken into account. The problem is solved by means of the boundary element method. To estimate the changes of temperature due to the change of local geometry of internal boundary Γ c the implicit variant of shape sensitivity analysis is applied. In the final part, the results of computations are shown and the conclusions are formulated.
14
Content available remote Numerical solution of the inverse parametric problem using the boundary element method
100%
Majchrzak E. , Freus K.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2002
|
tom Vol. 1, nr 1
125--132
EN
In the paper the application of the boundary element method for numerical solution of the inverse parametric problem is presented, this means the temperature dependent thermal conductivity is identified. The thermal conductivity of the material appears in the fundamental Fourier law and also in the basic energy equation (the Kirchhoff-Fourier equation). This parameter is determined on the basis of physical experiments. The numerical identification of the thermal conductivity is possible on the basis of the knowledge of temperature field in the\ domain considered.
15
Content available remote Application of the rational B-spline curves for description of complex domain shape
100%
Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2008
|
tom Vol. 7, nr 1
35-41
16
Content available Determination of the temperature field in burned and healthy skin tissue using the boundary element method. Part 2
100%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 3
47--54
EN
In the paper, the position of the boundary between burned and healthy tissue is described by the NURBS curve. The temperature field in the domain is calculated by means of the boundary element method. The influence of discretization on the temperature distribution in the burned and healthy skin tissue is analysed. Different numbers of boundary elements and internal cells are taken into account. In the final part of the paper the examples of computations are shown.
17
Content available A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method
100%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2017
|
tom Vol. 16, nr 2
67--76
EN
The aim of this paper is to create an optimal shape of the 2D domain that is described by the Non-Uniform Rational B-Splines (NURBS) curves. This work presents a method based on the topological derivative for the Laplace equation that determines the sensitivity of a given cost function to the change of its topology. As a numerical approach, the boundary element method is considered. To check the effectiveness of the proposed approach, the example of computations was carried out.
18
Solution of parametric inverse problem using the boundary element method
100%
Majchrzak E. , Freus K.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2000
|
tom Vol. 263, z. 63
9-14
19
Content available Determination of the temperature field in burned and healthy skin tissue using the boundary element method. Part 1
80%
Freus K. , Freus S. , Majchrzak E.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
tom Vol. 12, nr 3
39--46
EN
In the paper the burned and healthy layers of skin tissue are considered. The temperature distribution in these layers is described by the system of two Pennes equations. The governing equations are supplemented by the boundary conditions. On the external surface the Robin condition is known. On the surface between burned and healthy skin the ideal contact is considered, while on the internal surface limiting the system the body temperature is taken into account. The problem is solved by means of the boundary element method.
20
Content available remote Application of the BEM for numerical solution of nonlinear diffusion equation
80%
Majchrzak E. , Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2007
|
tom Vol. 6, nr 1
159-167
EN
In the paper the nonlinear diffusion equation is considered, this means the volumetric specific heat and thermal conductivity are temperature dependent. To solve the problem by means of the boundary element method the Kirchhoff transformation is introduced and for each time step the mean values of these parameters are taken into account. In the final part of the paper the results of computations are shown.
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