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  1. 3 Czasopismo Techniczne. Nauki Podstawowe
  2. 3 International Journal of Applied Mathematics and Computer Science
  3. 3 Technical Transactions. Fundamental Sciences
  4. 2 Fasciculi Mathematici
  5. 2 Opuscula Mathematica
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  1. 4 Koroński J.
  2. 2 Pachpatte B. G.
  3. 1 Babichev A. V.
  4. 1 Biały J.
  5. 1 Bielski A.
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  1. 1 2024
  2. 2 2021
  3. 1 2020
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  5. 3 2016
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1
Content available Varying coefficients in parallel shared-memory variational splitting solvers for non-stationary Maxwell equations
Łoś Marcin, Woźniak Maciej, Paszyński Maciej
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2024
|
Vol. 72, nr 3
art. no. e149179
EN
Direction-splitting implicit solvers employ the regular structure of the computational domain augmented with the splitting of the partial differential operator to deliver linear computational cost solvers for time-dependent simulations. The finite difference community originally employed this method to deliver fast solvers for PDE-based formulations. Later, this method was generalized into so-called variational splitting. The tensor product structure of basis functions over regular computational meshes allows us to employ the Kronecker product structure of the matrix and obtain linear computational cost factorization for finite element method simulations. These solvers are traditionally used for fast simulations over the structures preserving the tensor product regularity. Their applications are limited to regular problems and regular model parameters. This paper presents a generalization of the method to deal with non-regular material data in the variational splitting method. Namely, we can vary the material data with test functions to obtain a linear computational cost solver over a tensor product grid with non-regular material data. Furthermore, as described by the Maxwell equations, we show how to incorporate this method into finite element method simulations of non-stationary electromagnetic wave propagation over the human head with material data based on the three-dimensional MRI scan.
2
Content available A research study on unsteady state convection diffusion flow with adoption of the finite volume technique
Patel Manoj R., Pandya Jigisha U.
Journal of Applied Mathematics and Computational Mechanics
|
2021
|
Vol. 20, nr 4
65--76
EN
This research paper is an attempt to solve the unsteady state convection diffusion one dimension equation. It focuses on the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique. The simulation of the unsteady state convection diffusion problem with a known actual solution is also used to validate both the techniques, respectively, the fully implicite hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique by giving a particular example and solving it using the appropriate, particular technique. It is observed that the numerical scheme is an outstanding deal with the exact solution. Numerical results and graphs are presented for different Peclet numbers.
3
Content available Singular integration in boundary element method for Helmholtz equation formulated in frequency domain
Rymarczyk Tomasz, Sikora Jan
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
|
2021
|
T. 11, nr 4
4--8
EN
Two ways of approximation of the BEM kernel singularity are presented in this paper. Based on these approximations extensive error analysis was carried on. As a criterion the preciseness and simplicity of approximation were selected. Simplicity because such approach would be applied for the tomography problems, so time of execution plays particularly significant role. One of the approximations which could be applied for the wide range of the arguments of the kernel were selected.
PL
Dwie metody aproksymacji osobliwości funkcji Greena zaproponowano w tej pracy. Bazując na tych aproksymacjach dokonano wnikliwej analizy błędów. Jako kryterium wybrano dokładność i prostotę zaproponowanych aproksymacji. Prostotę dlatego, że takie podejście będzie proponowane w zagadnieniach tomograficznych. Tak więc czas odgrywa zasadniczą rolę. Wybrano aproksymację, która może być stosowana dla szerokiego zakresu argumentów.
4
Content available Theoretical Analysis and Experimental Verification of Top Orthogonal to Bottom Arrays of Conducting Strips on Piezoelectric Slab
Tasinkevych Yuriy, Trots Ihor, Tymkiewicz Ryszard
Archives of Acoustics
|
2020
|
Vol. 45, No. 3
433--444
EN
The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.
5
Content available Parameters affecting water hammer in plastic pipelines
Urbanowicz K., Firkowski M.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
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2018
|
nr 54 (126)
35--43
EN
Pressure pipes made of selected plastics are widely used in current water supply systems. Unfortunately, the theoretical basis for modeling transient flows in these pipes has not been clarified yet. For simplified one-dimensional numerical modeling, a model is commonly used in which the total deformation of the pipe walls is expressed by the sum of instantaneous and retarded deformations. One of the main problems lies in the correct experimental determination of the creep function defining the properties of the polymer. The influence of other parameters on which the numerical solution of the method of characteristics is based is the subject of the research presented in this paper.
6
Content available Zastosowanie algebr hiperzespolonych w przetwarzaniu sygnałów
Błaszczyk Ł.
Technical Issues
|
2016
|
nr 3
13--18
EN
The subject of this paper is the application of hypercomplex algebras (in particular quaternions and octonions) in the analysis of time-invariant linear systems. We present the Cayley-Dickson construction of hypercomplex algebras and its important properties. Moreover, we formulate the concept of quaternion and octonion Fourier transform and their properties important from the signal processing point of view. We present an overview of known quaternion Fourier transform applications in the analysis of systems and partial differential equations of two variables. We also point out the direction of further work in the subject of application of the octonion Fourier transform in system analysis and analysis of partial differential equations of three variables. Such considerations are possible thanks to recently proved properties of octonion Fourier transform, which are also stated in this paper.
7
Content available General remarks on dynamic projection method
Leble S.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2016
|
Vol. 20, No 2
113--130
EN
A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.
8
Content available A new imaging algorithm for electric capacitance tomography
Pańczyk M., Sikora J.
Prace Instytutu Elektrotechniki
|
2016
|
Z. 274
27--41
EN
A new imaging algorithm of permittivity for Electrical Capacitance Tomography (ECT) was proposed in this paper. Some aspects of sensitivity analysis and the application of adjoint variables were discussed. In the final section of this paper some advantages and disadvantages were shown.
PL
W pracy przedstawiono „nowy” algorytm obrazowania przenikalności elektrycznej w Elektrycznej Tomografii Pojemnościowej. Omówiono aspekty związane z analizą wrażliwościową i zmienna sprzężoną. Przedstawiono jej interpretację fizyczną. Wskazano na zalety i wady zaproponowanej metody obrazowania.
9
Content available Analytic continuation of solutions of some nonlinear convolution partial differential equations
Tahara H.
Opuscula Mathematica
|
2015
|
Vol. 35, no. 5
739--773
EN
The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summa-bility theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
10
Content available remote Stanisław Zaremba (1863‒1942) and his results in the field of differential equations
Koroński J.
Czasopismo Techniczne. Nauki Podstawowe
|
2015
|
Y. 112, iss. 2-NP
207--217
EN
The subject of the paper is presentation of the publications of Stanisław Zaremba in the field of partial differential equations. We present selected results in detail. Zaremba published about 120 works. Among them more than 60 were devoted to partial differential equations.
PL
Artykuł poświęcony jest prezentacji publikacji Stanisława Zaremby w dziedzinie równań różniczkowych cząstkowych. Wybrane rezultaty zaprezentowano bliżej. Zaremba opublikował około 120 prac, z których ponad 60 jest poświęconych równaniom różniczkowym cząstkowym.
11
Content available remote Stanisław Kępiński (1867‒1908) and his papers in the field of differential equations
Koroński J.
Czasopismo Techniczne. Nauki Podstawowe
|
2015
|
Y. 112, iss. 2-NP
201--206
EN
The subject of this paper is an analysis of the publications of Stanisław Kępiński in the field of ordinary and partial differential equations. In particular we present part I and part II of the monograph (textbook) of Stanisław Kępiński on the ordinary and partial differential equations.
PL
Artykuł poświęcony jest prezentacji publikacji Stanisława Kępińskiego w dziedzinie zwyczajnych i cząstkowych równań różniczkowych. W pracy prezentujemy zwłaszcza dwuczęściową monografię (podręcznik) z równań różniczkowych zwyczajnych i cząstkowych.
12
Content available Simulating In-Situ Leaching Process Using COMSOL Multiphysics
Mukhanov B. K., Omirbekova Z. Z., Usenov A. K., Wójcik W.
International Journal of Electronics and Telecommunications
|
2014
|
Vol. 60, No. 3
213-217
EN
The paper deals with simulation of in-situ uranium leaching technological process, collecting data for forecasting and leaching process control. It provides numerical simulation of uranium in-situ leaching (ISL) using Comsol Multiphysics software package a pplication. Previous studies evaluated main hydrodynamic characteristics of wells and reservoirs, such as the coefficient of resistance and the saturation recovery; while this paper is concerned with determining the changes in process variables in the wells during operation.
13
Content available remote Władysław Zajączkowski and differential equations in Poland in the second half on the nineteenth century
Koroński J.
Czasopismo Techniczne. Nauki Podstawowe
|
2014
|
R. 111, z. 1-NP
107--117
EN
The paper contains some scientific information on Władysław Zajączkowski (1837–1898) and on his first Polish monograph about ordinary and partial differential equations. Moreover, the aim of this paper is a presentation of selected scientific results of Polish mathematicians publishing in the nineteenth century in the field of ordinary and partial differential equations. Some more details about the publications on differential equations in the 19th century written by Polish mathematicians can be found in [3‒9].
PL
W artykule zawarto pewne informacje naukowe o Władysławie Zajączkowskim i jego pierwszej polskiej monografii z równań różniczkowych zwyczajnych i cząstkowych. Ponadto przedmiotem pracy jest prezentacja wybranych rezultatów naukowych matematyków polskich publikujących w drugiej połowie dziewiętnastego wieku w dziedzinie równań różniczkowych zwyczajnych i cząstkowych. Pewne szczegółowe informacje o publikacjach z równań różniczkowych w dziewiętnastym wieku napisanych przez matematyków polskich można znaleźć w [3‒9].
14
Content available remote Newton’s method for first-order stochastic functional partial differential equations
Wrzosek M.
Commentationes Mathematicae
|
2014
|
Vol 54, No. 1
51--64
EN
We apply Newton’s method to hyperbolic stochastic functional partial differential equations of the first order driven by a multidimensional Brownian motion. We prove a first-order convergence and a second-order convergence in a probabilistic sense.
15
Zastosowanie równań różniczkowych cząstkowych drugiego stopnia w zagadnieniach technicznych
Biały J., Gołębiowski J.
Zeszyty Naukowe / Wyższa Szkoła Oficerska Sił Powietrznych
|
2013
|
Nr 1
9--21
PL
Niniejszy artykuł ma za zadanie przybliżyć zagadnienie dotyczące rozwiązania równania struny i membrany metodą Fouriera, pokazać sposób jej wykorzystania w różnych dziedzinach.
EN
The following article is intended to focus on the problem pertaining to the solution of string and membrane equation with Fourier’s method as well as to show its applications in various fields.
16
Content available remote Mirosław Krzyżański (1907-1965) i jego monografia z równań różniczkowych cząstkowych
Koroński J.
Kwartalnik Historii Nauki i Techniki
|
2013
|
R. 58, nr 4
7--28
EN
The present paper contains a spacious biography of Mirosław Krzyżański (1907-1965) and some information on the monograph about partial differential equ ations of second order, which was edited: in Polish - part I in 1957, and part II in 1962, and in English by PWN in 1971. Moreover in the paper some information on the most important original scientific results and bibliography of M. Krzyżański are given.
17
Content available remote Juliusz Schauder, topology of function spaces and Partial Differential Equations
Mawhin J.
Wiadomości Matematyczne
|
2012
|
T. 48, Nr 2
173--183
18
Content available remote Modeling the flow of compressible media in a vessel by means of Simulin S-functions
Ozana S., Pies M.
Przegląd Elektrotechniczny
|
2012
|
R. 88, nr 5b
183-186
EN
The paper deals with modeling the flow of compressible media in a vessel, while elasticity of the vessel can change. It presents mathematical model of a pipeline as system with distributed parameters, consisting of three partial differential equations and two additional equations which describes density and area as functions of pressure and temperature. The solution of the problematic is achieved by means of Matlab&Simulink environment, particularly by use of S-functions and finite difference method (FDM). The paper includes a case study when a set of pressure impulses is brought to the model of a vessel. As a result, media pressure, temperature and velocity are displayed over the time and along the pipeline.
PL
W pracy opisane jest modelowanie przepływu ściśliwego medium w naczyniu kwionośnym (żyle), gdzie elastyczność naczynia może być zmienna. Przedstawiono model matematyczny rurociągu z rozłożonymi parametrami, który składa się z trzech równań różniczkowo cząstkowych i dwa dodatkowe równania, które opisują gęstości i powierzchnię w funkcji ciśnienia I temperatury. Problem jest rozwiązywany za pomocą środowiska Matlab & Simulink, w szczególności poprzez wykorzystanie S-funkcji i metody różnic skończonych (finite difference method - FDM). Artykuł zawiera analizę przypadku, gdy zestaw impulsów ciśnienia doprowadza się do modelu naczynia. Wynikiem analizy są przebiegi czasowe ciśnienia, temperatury i prędkości wzdłuż naczynia krwionośnego.
19
Content available Impulsive and periodic class of solutions for hydrodynamic theory of lubrication
Wierzcholski K., Miszczak A.
Journal of KONES
|
2012
|
Vol. 19, No. 4
651-658
EN
In this paper, two different classes of lubricant flow conditions are basically indicated, i.e. for periodic solutions when pressure values and other flow parameters change periodically and for non-periodic solutions in the case of lubricating in the conditions of impulses and strokes. The Authors formulate the primary problem in the form of a system of 9 nonlinear non-homogeneous partial differential equations with variable and random coefficients in a curvilinear orthogonal system of coordinates which is supplemented with suitable constitutive dependences and conjugated with magnetic field equations with the Ohm equation. These equations include the following: three conservation equations of the lubricating liquid momentum, the stream continuity equation, the energy conservation equation, three equilibrium equations of the thin elastic superficial layer that are reduced to the differential equation in displacements, the heat transfer equation of the superficial layer that is flown around by the lubricating liquid. The following include those equations that describe constitutive dependences the Rivlin-Ericksen equation of physical dependences for viscoelastic ferrofluid, the equation of the physical dependences of the superficial layer of the surfaces lubricated, the equation of the physical dependences of the magnetic field. The unknown values of the material coefficients shall be determined experimentally. The following 9 unknowns are determined from the system of partial differential equations: three velocity components of the lubricating liquid, the hydrodynamic pressure, the temperature in the lubricating liquid, the three components of the superficial layer displacement and the temperature in the superficial layer. The mathematical solution of the problem presented requires a number of boundary conditions to be imposed. The Authors foresee quasi-analytical solutions of the system described of partial differential equations.
20
Content available A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics
Rafajłowicz E., Styczeń K., Rafajłowicz W.
International Journal of Applied Mathematics and Computer Science
|
2012
|
Vol. 22, no. 2
313-326
EN
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.
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