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  1. 4 Journal of Applied Mathematics and Computational Mechanics
  2. 3 Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
  3. 3 Przegląd Elektrotechniczny
  4. 3 Scientific Research of the Institute of Mathematics and Computer Science
  5. 1 Annales Polonici Mathematici
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  1. 1 2023
  2. 2 2019
  3. 1 2018
  4. 1 2017
  5. 3 2016
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  1. 5 Freus S.
  2. 4 Freus K.
  3. 3 Majchrzak E.
  4. 2 Pawłowski S.
  5. 2 Plewako J.
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1
Content available remote Infinite dimension of solutions of the Dirichlet problem
100%
Ryazanov V.
Open Mathematics
|
2015
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tom 13
|
nr 1
EN
It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
2
Content available remote Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
100%
Pliś M. E. , Ziemian B.
|
1997
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tom 67
|
nr 1
31-41
EN
We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.
3
Content available remote The Multipole method for the Laplace equation in domains with polyhedral corners
100%
Skorokhodov S. L. , Vlasov V. I.
Computer Assisted Mechanics and Engineering Sciences
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2004
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tom Vol. 11, No. 2-3
223-238
EN
A new analytic-numerical method has been developed for solving the Laplace equation in domains with cones of arbitrary base, in particular with polyhedral corners. The solution is represented as an expansion involving singular functions (the Multipoles), which play the role of basic functions. The method enables to find these functions explicitly and to compute efficiently their singularity exponents. The method possesses exponential rate of convergence and provides precise computation of the solution, its derivatives and intensity factors at the edges and at the corner point. In addition, an asymptotic expansion of the solution near the edges of polyhedral corner has been obtained.
4
Content available remote Cross-properties of the effective conductivity of the regular array of ideal conductors
100%
Gluzman S. , Mityushev V. , Nawalaniec W.
Archives of Mechanics
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2014
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tom Vol. 66, nr 4
287--301
EN
We present an accurate expression for the effective conductivity of a regular square-lattice arrangement of ideally conducting cylinders, valid for arbitrary concentrations. The formula smoothly interpolates between the two asymptotic expressions derived for low and high concentrations of the cylinders. Analogy with critical phenomena is suggested and taken to the extent of calculating the superconductivity critical exponent and the particle-phase threshold from the very long expansions in concentration. The obtained formula is valid for all concentrations including touching cylinders, hence it completely solves with high accuracy the problem of the effective conductivity for the square array.
5
Content available remote Shape sensitivity analysis with respect to the parameters of internal hole
100%
Majchrzak E. , Tarasek D.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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tom Vol. 7, nr 1
129-140
EN
The Laplace equation describing temperature field in 2D domain supplemented by adequate boundary conditions is considered. The aim of investigations is to estimate the changes of temperature due to changes of shape parameter (e.g. radius or position of internal hole). To solve the problem, the implicit differentiation method of shape sensitivity analysis coupled with the boundary element method is applied.
6
Content available Comparison of efficiency of electrostatic micro-actuators for precise positioning
100%
Štarman V. , Kacerovský J. , Jansa J. , Karban P. , Doležel I.
Poznan University of Technology Academic Journals. Electrical Engineering
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2013
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tom No. 73
29--34
EN
Comparison of several types of electrostatic micro-actuators is carried out, particularly with respect to their resultant force effects. The continuous mathematical model of such actuators is mostly described by the Laplace equation. In this paper, its numerical solution is performed by a fully adaptive higher-order finite element method, using a code developed by the authors. The methodology is illustrated by typical examples whose results are discussed.
7
Content available Trefftz method for polynomial-based boundary identification in two-dimensional Laplacian problems
100%
Hożejowski L.
Journal of Theoretical and Applied Mechanics
|
2016
|
tom Vol. 54 nr 3
935--944
EN
The paper addresses a two-dimensional boundary identification (reconstruction) problem in steady-state heat conduction. Having found the solution to the Laplace equation by superpositioning T-complete functions, the unknown boundary of a plane region is approximated by polynomials of an increasing degree. The provided examples indicate that sufficient accuracy can be obtained with a use of polynomials of a relatively low degree, which allows avoidance of large systems of nonlinear equations. Numerical simulations for assessing the performance of the proposed algorithm show better than 1% accuracy after a few iterations and very low sensitivity to small data errors.
8
Content available remote Level Set Method in Inverse Problem Solution
88%
Stasiak M. , Berowski P.
|
2009
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tom Vol. 17, nr 1
95-106
EN
The optimal shape design of the capacitor with Laplace equation of state and inverse problem solution in Electrical Impedance Tomography using level set method are presented in the paper. The inverse problem solution determines the positions of capacitor plates, which were optimized to achieve required potential distribution, while the inverse problem solution in EIT enables the identification of the size and the position of internal areas with different conductivity.
9
Content available remote Contact angles of protein black foam films under dynamic and equilibrium conditions
88%
Nedyalkov M. , Sultanem C. , Benattar J.-J.
Open Chemistry
|
2007
|
tom 5
|
nr 3
748-765
EN
The contact angles of protein Newton black foam films from ALG (alpha-lactalbumin), BLG (beta-lactoglobulin) and BSA (bovine serum albumin) are measured here within. The measurements are carried out under dynamic and equilibrium conditions. For all proteins, a strong hystheresis effect of the contact angle is observed under dynamic conditions. An attempt is made to explain these results by the slow adsorption and desorption kinetics of the protein bilayers and by the dynamic structure and the rheology of the protein network forming the bubble walls. In addition, we propose a modification of the experimental device reported previously for contact angle measurements of large flat films in equilibrium. The advantages of this method are discussed in detail. Some shortcomings (precision, reproducibility) of this preliminary variant of the device in this initial stage of its application, do not allow one to draw reliable conclusions about the interactions of these films. Some improvements of the measurement quality are proposed. [...]
10
Content available Applying the topological derivative and the boundary element method to design of shape of the heat exchanger
88%
Freus K. , Freus S.
|
|
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.
11
Content available Fourier Image Methods for Evolution Equations of Deep-Water Waves
88%
Jankowski J. , Leszczyński H.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2019
|
tom Vol. 23, No 3
261--268
EN
The velocity potential of the fluid satisfies the Laplace equation with nonlocal boundary conditions on a free surface. This differential problem is transformed to an evolution equation in Fourier variables. The Fourier transform images of boundary functions are approximated by Picard's iterations and the method of lines on meshes related to roots of Hermite polynomials. Due to convolutions of sine and cosine functions the integral terms of Picard's iterations reveal unexpected instabilities for wave numbers in a neighborhood of zero.
12
Content available remote Równanie Laplace’a w ujęciu pochodnych niecałkowitego rzędu
75%
Zawadzki A. , Włodarczyk M. , Różowicz S.
Przegląd Elektrotechniczny
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2023
|
tom R. 99, nr 4
107--110
PL
W pracy przedstawiono równanie Laplace’a w ujęciu pochodnych niecałkowitego rządu oraz podjęto próbę znalezienia analitycznego rozwiązania takiego równania. Do rozwiązania zastosowano metodę separacji zmiennej (metodę Fouriera).
EN
The paper attempts of Laplace type of a linear fractional order differential equation and find an analytical solution. To solve this equation the method of variable separation (Fourier method) was used.
13
Content available Algorithm of rebuilding a boundary of domain during creation of an optimal shape
75%
Freus K. , Freus S.
Journal of Applied Mathematics and Computational Mechanics
|
2016
|
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.
14
Content available Analytical validation of the Finite Element Method model for Laplace equation
75%
Węgrzyn-Skrzypczak E. , Skrzypczak T.
Journal of Applied Mathematics and Computational Mechanics
|
2019
|
tom Vol. 18, nr 3
97--106
EN
The presented paper is focused on the comparison of the numerical solution of the Laplace equation in a two-dimensional space with the results obtained with the use of the analytical method. The results of the numerical model are computed on the base of the Finite Element Method. The analytical solution of the considered equation is obtained using the Fourier series. Finally the results of both methods are compared in order to verify the accuracy of numerical implementation.
15
Content available remote Application of boundary element method to shape sensitivity analysis
75%
Majchrzak E. , Dziewoński M. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2005
|
tom Vol. 4, nr 1
137-146
EN
In the paper the boundary element method to shape sensitivity analysis is applied. The Laplace equation is analyzed and the aim of investigations is to estimate the changes of temperature in the 2D domain due to the change of local geometry of the boundary. Here the implicit differentiation method of shape sensitivity analysis is used. In the final part of the paper the example of numerical computations is shown.
16
Content available Homotopy perturbation method in the heat conduction problems
75%
Hetmaniok E. , Nowak I. , Słota D. , Wituła R.
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
|
2011
|
tom z. 1
109--120
EN
In this paper an application of the homotopy perturbation method for solving the steady state and unsteady state heat conduction problem is presented.
PL
W artykule przedstawiono zastosowanie homotopijnej metody perturbacyjnej do rozwiązania zagadnień ustalonego oraz nieustalonego przewodzenia ciepła.
17
Content available remote On the nonexistence of positive solution of Laplace equation in half-space Rn with a nonlinear Neumann boundary condition
75%
Binh D. T. T. , Long N. T.
|
2000
|
tom Vol. 33, nr 2
365-372
18
Content available remote Shape sensitivity analysis : implicit approach using boundary element method
63%
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
Content available remote Porównanie efektywności iteracyjnej metody rozwiązań fundamentalnych i metody elementów skończonych w analizie zagadnień elektrostatyki
63%
Pawłowski S. , Plewako J. , Grodzki P.
Przegląd Elektrotechniczny
|
2017
|
tom R. 93, nr 12
135--138
PL
(MES) na podstawie analizy rezultatów testów numerycznych przeprowadzonych na modelowym zagadnieniu elektrostatyki. Stwierdzono, że za pomocą IMRF można uzyskać rozwiązanie o danej dokładności w czasie wielokrotnie krótszym (nawet kilkadziesiąt razy) niż za pomocą MES.
EN
The article presents efficiency comparison of the iterative method of fundamental solutions (IMFS) and finite element method (FEM), based on the analysis of numerical tests results obtained for the model of electrostatics problem. It has been found, that applying the IMFS a solution of assumed accuracy could be obtained numerous times shorter (even several dozen times) than using the FEM.
20
Content available remote Obliczanie współczynników pojemnościowych układu ciał przewodzących Iteracyjną Metodą Rozwiązań Fundamentalnych
63%
Pawłowski S. , Plewako J.
Przegląd Elektrotechniczny
|
2018
|
tom R. 94, nr 12
210--213
PL
W pracy zaprezentowano procedurę obliczania współczynników pojemnościowych trójwymiarowych układów elektrostatycznych, opartą na idei Iteracyjnej Metody Rozwiązań Fundamentalnych. Procedura ta pozwala na bezpośrednie wyznaczanie ładunków zgromadzonych na powierzchniach ciał przewodzących bez konieczności obliczania rozkładu pola elektrycznego. Umożliwia ona także ustalenie żądanej dokładności rozwiązania. W przeprowadzonym teście numerycznym stwierdzono bardzo dobrą zbieżność i efektywność metody.
EN
A procedure for calculating the capacitive coefficients of three-dimensional electrostatic systems, based on the idea of the Iterative Method of Fundamental Solutions is presented in the paper. This procedure allows direct determination of charges on the surfaces of conductive bodies without the need to calculate the distribution of the electric field. It also allows you to determine the desired accuracy of the solution. The numerical test performed showed very good convergence and efficiency of the method.
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