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Wyświetlanie 1-15 z 29
Tytuł:
Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
Autorzy:
Pliś, Maria Ewa
Ziemian, Bogdan
Powiązania:
https://bibliotekanauki.pl/articles/1294724.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Borel resummation
formal solutions
Laplace equation
Opis:
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.
Źródło:
Annales Polonici Mathematici; 1997, 67, 1; 31-41
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A counterexample to the $L^{p}$-Hodge decomposition
Autorzy:
Hajłasz, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/1359021.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonuniqueness
Dirichlet problem
Laplace equation
Hodge decomposition
Opis:
We construct a bounded domain $Ω ⊂ ℝ^2$ with the cone property and a harmonic function on Ω which belongs to $W_0^{1,p}(Ω)$ for all 1 ≤ p < 4/3. As a corollary we deduce that there is no $L^p$-Hodge decomposition in $L^{p}(Ω,ℝ^2)$ for all p > 4 and that the Dirichlet problem for the Laplace equation cannot be in general solved with the boundary data in $W^{1,p}(Ω)$ for all p > 4.
Źródło:
Banach Center Publications; 1996, 33, 1; 79-83
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Identification of polygonal domains using PIES in inverse boundary problems modeled by 2D Laplaces equation
Autorzy:
Zieniuk, E.
Bołtuć, A.
Powiązania:
https://bibliotekanauki.pl/articles/1964153.pdf
Data publikacji:
2005
Wydawca:
Politechnika Gdańska
Tematy:
parametric integral equation system (PIES)
inverse problems
Laplace's equation
Opis:
The paper presents an original method to identify polygonal boundary geometry in 2D boundary problems defined by Laplace's equation using a parametric integral equation system (PIES). In the PIES, the polygonal boundary shape is defined mathematically by means of parametric linear segments, with a small number of corner points being posed. Identification of the polygonal boundary is reduced to identification of the corner points. Finally, the solution of the problem is reduced to the solution of a non-linear system of algebraic equations. Coordinates of identified corner points are obtained after solving the system of equations.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2005, 9, 4; 415-426
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Anisotropic p-Laplace Equations on long cylindrical domain
Autorzy:
Jana, Purbita
Powiązania:
https://bibliotekanauki.pl/articles/29519481.pdf
Data publikacji:
2024
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
pseudo p-Laplace equation
cylindrical domain
asymptotic analysis
Opis:
The main aim of this article is to study the Poisson type problem for anisotropic p-Laplace type equation on long cylindrical domains. The rate of convergence is shown to be exponential, thereby improving earlier known results for similar type of operators. The Poincaré inequality for a pseudo p-Laplace operator on an infinite strip-like domain is also studied and the best constant, like in many other situations in literature for other operators, is shown to be the same with the best Poincaré constant of an analogous problem set on a lower dimension.
Źródło:
Opuscula Mathematica; 2024, 44, 2; 249-265
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Software for determination of surface tension with sessile drop method
Autorzy:
Lytvyn, M.
Powiązania:
https://bibliotekanauki.pl/articles/1940693.pdf
Data publikacji:
2017
Wydawca:
Politechnika Gdańska
Tematy:
sessile drop method
surface tension calculation
Young-Laplace equation
Opis:
The sessile drop method was implemented to calculate the values of the surface tension coefficient of liquid metals. Appropriate software was developed to increase the data processing efficiency and the accuracy of the obtained results. This paper provides information on the structure and applications of the designed programs as well as the underlying mathematical models used during computations. Since the determination of the surface tension coefficient in this study is based on the recognition of drop outlines from a digital image, the problems of calibration and appropriate photography mode adjustments are mentioned in this paper. In addition, the methods of controlling the research equipment using Arduino shields are described. Finally, the research results are presented in the form of graphs which show the temperature dependence of the studied parameters of metallic samples and compared with the literature data.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2017, 21, 1; 65-76
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trefftz method for polynomial-based boundary identification in two-dimensional Laplacian problems
Autorzy:
Hożejowski, L.
Powiązania:
https://bibliotekanauki.pl/articles/280415.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
inverse geometry problem
boundary identification
Trefftz method
Laplace equation
Opis:
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.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 3; 935-944
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparison of efficiency of electrostatic micro-actuators for precise positioning
Autorzy:
Štarman, V.
Kacerovský, J.
Jansa, J.
Karban, P.
Doležel, I.
Powiązania:
https://bibliotekanauki.pl/articles/377434.pdf
Data publikacji:
2013
Wydawca:
Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Tematy:
electrostatic micro-actuator
Laplace equation
higher-order finite element method
Opis:
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.
Źródło:
Poznan University of Technology Academic Journals. Electrical Engineering; 2013, 73; 29-34
1897-0737
Pojawia się w:
Poznan University of Technology Academic Journals. Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Homotopy perturbation method in the heat conduction problems
Homotopijna metoda perturbacyjna w zagadnieniach przewodzenia ciepła
Autorzy:
Hetmaniok, E.
Nowak, I.
Słota, D.
Wituła, R.
Powiązania:
https://bibliotekanauki.pl/articles/87322.pdf
Data publikacji:
2011
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
przewodzenie ciepła
równanie Laplace'a
teoria perturbacji
heat conduction
Laplace equation
perturbation theory
Opis:
In this paper an application of the homotopy perturbation method for solving the steady state and unsteady state heat conduction problem is presented.
W artykule przedstawiono zastosowanie homotopijnej metody perturbacyjnej do rozwiązania zagadnień ustalonego oraz nieustalonego przewodzenia ciepła.
Źródło:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska; 2011, 1; 109-120
2084-073X
Pojawia się w:
Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Applying the topological derivative and the boundary element method to design of shape of the heat exchanger
Autorzy:
Freus, K.
Freus, S.
Powiązania:
https://bibliotekanauki.pl/articles/122334.pdf
Data publikacji:
2015
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
topological derivative
topological sensitivity
Laplace equation
boundary element method
heat transfer
Opis:
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.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 2; 5-12
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fourier image methods for evolution equations of deep-water waves
Autorzy:
Jankowski, Jan
Leszczyński, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/1955223.pdf
Data publikacji:
2019
Wydawca:
Politechnika Gdańska
Tematy:
wave evolution
Laplace equation
Fourier transform
method of lines
Gauss-Hermite quadrature
Opis:
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.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2019, 23, 3; 261-268
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical validation of the Finite Element Method model for Laplace equation
Autorzy:
Węgrzyn-Skrzypczak, Ewa
Skrzypczak, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/122738.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Laplace equation
Fourier’s method
Finite Element Method
równanie Laplace'a
metoda Fouriera
metoda elementów skończonych
Opis:
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.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 3; 97-106
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Algorithm of rebuilding a boundary of domain during creation of an optimal shape
Autorzy:
Freus, K.
Freus, S.
Powiązania:
https://bibliotekanauki.pl/articles/122780.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Laplace equation
boundary element method
heat transfer
topological-shape sensitivity method
równanie Laplace'a
metoda elementów brzegowych
wymiana ciepła
Opis:
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.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 17-24
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A design of an optimal shape of domain described by NURBS curves using the topological derivative and boundary element method
Autorzy:
Freus, K.
Freus, S.
Powiązania:
https://bibliotekanauki.pl/articles/122807.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Laplace equation
boundary element method
topological derivative
NURBS curves
równanie Laplace'a
metoda elementów brzegowych
pochodna topologiczna
krzywa NURBS
Opis:
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.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 67-76
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of an optimal shape of domain using the topological derivative and the Boundary Element Method
Autorzy:
Freus, K.
Freus, S.
Powiązania:
https://bibliotekanauki.pl/articles/122328.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
topological derivative
topological sensitivity
topology optimization
heat transfer
Laplace equation
boundary element method
pochodna topologiczna
wrażliwość topologiczna
optymalizacja topologiczna
wymiana ciepła
równanie Laplace'a
metoda elementów brzegowych
Opis:
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.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 4; 41-48
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of inverse heat conduction equation with the use of Chebyshev polynomials
Autorzy:
Joachimiak, M.
Frąckowiak, A.
Ciałkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/239926.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Laplace’s equation
boundary inverse problem
quasi-Cauchy problem
stability of the inverse problem
równanie Laplace'a
brzegowe zagadnienie odwrotne
Problem Quasi-Cauchy'ego
Opis:
A direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.
Źródło:
Archives of Thermodynamics; 2016, 37, 4; 73-88
1231-0956
2083-6023
Pojawia się w:
Archives of Thermodynamics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 29

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