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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 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
|
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.
3
Modelling of transient heat transfer in heterogeneous domain using the 1st scheme of the boundary element method
100%
Mochnacki B. , Freus S.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2001
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tom z. 72
213-217
4
Content available remote Metoda elementów brzegowych : opis modułu dyskretyzacji brzegu i wnętrza obszaru
100%
Mochnacki B. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2002
|
tom Vol. 1, nr 1
153--162
PL
Metoda elementów brzegowych wymaga dyskretyzacji brzegu rozpatrywanego obszaru, a w wielu zadaniach również jego wnętrza. W artykule przedstawiono opis jednego z modułów autorskiego programu komputerowego do wyznaczania ustalonych lub nieustalonych pól temperatury za pomocą tej metody. Jest to moduł wprowadzania kształtu brzegu obszaru (lub brzegów obszarów) i jego podziału na liniowe elementy brzegowe z przyporządkowaniem rodzaju warunku brzegowego. Dla zadań, gdzie jest to niezbędne, dokonywana jest dyskretyzacja wnętrza obszaru (lub obszarów) za pomocą liniowych trójkątnych elementów wewnętrznych. Działanie modułu zilustrowano przykładem dyskretyzacji brzegu i wnętrza obszaru płaskiego.
5
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.
6
Application of control volume method in numerical modelling of solidification (micro/macro approach)
100%
Ciesielski M. , Freus S.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2009
|
tom z. 95
77-78
7
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
|
tom Vol. 7, nr 1
43-48
8
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
|
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.
9
Content available remote Numerical simulation of transient heat diffusion using the BEM
100%
Mochnacki B. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2003
|
tom Vol. 2, nr 1
121--128
EN
The paper contains the short discussion of the scientific and practical results presented in the monograph (doctoral theses) "Theoretical and practical application of the BEM in numerical modelling of unsteady heat transfer" done by S. Freus. The main subject of the work is the application of the so-called I scheme of the boundary element method for numerical simulation of unsteady heat conduction in homogeneous and non-homogeneous solid bodies with complex shape (the 2D problems are discussed). The BEM algorithm constitutes a base for professional code construction. The user of the code introduces only the shape of domain considered and its thermophysical parameters, the parameters of boundary conditions and the initial one. The simulation process is realised self-actingly.
10
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
|
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.
11
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
|
2012
|
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.
12
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
13
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.
14
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.
15
Content available Temperature field in burned and healthy tissue : sensitivity analysis with respect to the thermal parameters
80%
Freus K. , Freus S. , Majchrzak E.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
tom Vol. 13, nr 3
47--58
EN
A non-homogeneous system being the composition of burn wound and healthy tissue is considered. The heat exchange between sub-domains and environment is described by the system of partial differential equations (the Pennes equations) supplemented by the assumed boundary conditions. Additional problems associated with sensitivity analysis with respect to thermal parameters occurring in the mathematical model are formulated. Both the basic problem and additional ones concerning the sensitivity with respect to selected parameters are solved using the boundary element method. In the final part of the paper the results of computations are shown.
16
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.
17
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.
18
Content available remote Shape sensitivity analysis : implicit approach using boundary element method
80%
Majchrzak E. , Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2011
|
tom Vol. 10, nr 1
151-161
EN
The Laplace equation (2D problem) supplemented by boundary conditions is analyzed. To estimate the changes of temperature in the 2D domain due to the change of local geometry of the boundary, the implicit method of sensitivity analysis is used. In the final part of the paper, the example of numerical computations is shown.
19
Temperature recovery method. New aspects and applications
80%
Mochnacki B. , Lara S. , Freus S.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2005
|
tom z. 86
71-74
EN
In the paper the certain problems connected with the temperature recovery method application in numerical modelling of solidification are discussed. The method can be a base of very effective numerical procedure supplementing the boundary element method algorithm for the Fourier equation determining the heat transfer processes in the domain of solid body. In this way the basic version of the BEM can be used for the simulation of solidification process. In the final part the example of applications is presented.
20
Identification of Temperature Dependent Thermal Conductivity Using The Bed
80%
Majchrzak E. , Freus K. , Freus S.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2002
|
tom z. 75
145-148
EN
The thermal conductivity of the material is the very essential thermophysical parameter appearing in the fundamental Fourier law and also in the basic energy equation (the Kirchhoff-Fourier equation). This parameter can be treated as a constant value but, as a rule, it is the temperature dependent function. The thermal conductivity is determined on the basic of physical experiments. From the mathematical point of view the identification of this parameter on the basis of the knowledge of temperature field in the domain considered belong to the group of the parametric inverse problems (1). In this paper the numerical algorithm of the discussed parameter identification is presented.
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