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1
Content available remote Solution of 2D hyperbolic equation by means of the BEM using discretization in time
Drozdek J., Lupa M., Ładyga E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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Vol. 8, nr 1
19-24
EN
The hyperbolic equation (2D problem) supplemented by adequate boundary and initial conditions is considered. To solve the problem the boundary element method using discretization in time is adapted. In the final part of the paper the example of computations is shown.
2
Content available remote Solution of 2D hyperbolic equation by means of the BEM using discretization in time - analysis of solution exactness
Drozdek J., Lupa M., Ładyga E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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Vol. 8, nr 1
25-32
EN
The hyperbolic equation (2D problem) supplemented by adequate boundary and initial conditions is considered. This equation is solved by means of the boundary element method using discretization in time. The aim of investigations is to analyze the influence of time step and the discretization assumed on the exactness of the obtained results.
3
Content available remote Heating of tissue by means of the electric field : numerical model basing on the BEM
Majchrzak E., Drozdek J., Paruch M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
99-110
EN
The domain of tissue is subjected to the action of electrodes located on the skin surface. External electric field causes the heat generation in tissue domain. The distribution of electric potential in domain considered is described by the Laplace equation, while the temperature field is described by the Pennes equation. These problems are coupled by source function being the additional component in Pennes equation and resulting from the electric field action. The coupled problem is solved using the boundary element method. In the final part of the paper the examples of computations are shown.
4
Content available remote Application of the dual reciprocity boundary element method for numerical modelling of solidification process
Majchrzak E., Drozdek J., Kałuża G., Poteralska J.
Archives of Foundry Engineering
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2008
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Vol. 8, iss. 4
99-104
EN
The dual reciprocity boundary element method is applied for numerical modelling of solidification process. This variant of the BEM is connected with the transformation of the domain integral to the boundary integrals. In the paper the details of the dual reciprocity boundary element method are presented and the usefulness of this approach to solidification process modelling is demonstrated. In the final part of the paper the examples of computations are shown.
5
Content available remote Numerical solution of bioheat transfer equation by means of the dual reciprocity BEM
Drozdek J., Majchrzak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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Vol. 6, nr 1
47-56
EN
Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. It results from the presence of internal heat sources in the biological tissue (metabolic and perfusion sources). In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As example, the problem of temperature field computations in heating biological tissue domain is solved.
6
Content available remote Computer implementation of the dual reciprocity BEM for 2D Poisson's equation
Majchrzak E., Drozdek J., Ładyga E., Paruch M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2006
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Vol. 5, nr 1
95-105
EN
In this paper the variant of the boundary element method called dual reciprocity BEM is presented. On the stage of numerical computations the DRBEM application for the Poisson equation allows to avoid the discretization of the interior of the domain considered. In the final part of the paper the results of computations are shown.
7
Content available remote Dual reciprocity boundary method for the Poisson equation
Majchrzak E., Drozdek J., Ładyga E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
129-136
EN
The standard boundary element method for Poisson equation requires the discretization of boundary and interior of the domain considered. In this paper the variant called dual reciprocity boundary element method is presented. On the stage of numerical computations this approach allows to avoid the discretization of the interior of domain. In the final part of the paper the example of computations and comparison of results obtained using the BEM and DRBEM are shown.
8
Content available remote Modelling of thermal processes occuring in the tissue with a tumor with regard to parameter sensitivity analysis
Majchrzak E., Paruch M., Drozdek J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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Vol. 3, nr 1
133--142
EN
The numerical algorithm based on the multiple reciprocity boundary element method is used for the temperature field computations in the non-homogeneous domain of healthy tissue and the tumor region. The thermophysical parameters of tumor, in particular the perfusion rate, the metabolic heat source and the thermal conductivity are essentially bigger than for healthy tissue. From the mathematical point of view the problem is described by the system of two Poisson's equations supplemented by the adequate boundary conditions. The main subject of the paper is the sensitivity analysis of temperature distribution with respect to the thermal parameters of tumor region and healthy tissue. In the final part of the paper the examples of computations are shown.
9
Content available remote Sensitivity analysis of temperature field in the tissue with a tumor
Majchrzak E., Paruch M., Drozdek J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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Vol. 2, nr 1
93--98
EN
The numerical algorithm based on the boundary element method is used for the temperature field computations in the non-homogeneous domain of healthy tissue and the tumor region. Thermophysical parameters of tumor region, in particular the perfusion coefficient and the metabolic heat source are essentially bigger than for healthy tissue. The values of these parameters are assumed to be constant. From the mathematical point of view the problem is described by the system of two Poisson’s equations supplemented by the adequate boundary conditions. The main subject of the paper is the sensitivity analysis of temperature distribution with respect to the constant source functions in the sub-domains considered. In the final part the examples of computations are shown.
10
Boundary Element Method For The Poisson Equation
Majchrzak E., Drozdek J., Lupa M.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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2002
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z. 75
149-154
EN
Application of the standard boundary element method for numerical solution of the Poisson equation requires discretization not only the boundary but also the interior of the domain considered. In this paper we present the variant of the BEM which requires only the boundary discretization. It is the essential advantage of the algorithm proposed in comparison with the classical one. In the final part of the paper the example of computations is shown.
11
Content available remote Application of the multiple reciprocity BEM for numerical solution of bioheat transfer equation
Majchrzak E., Drozdek J., Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2002
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Vol. 1, nr 1
113--124
EN
Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As the example, the problem of the pair of vessels (artery and vein) surrounded by the tissue is analyzed, and the temperature field in the tissue sub-domain is found.
12
Identyfication of initial codition using the 2nd scheme of the bem
Majchrzak E., Drozdek J.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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2000
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z. 63
15-22
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