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Wyświetlanie 1-15 z 21
Tytuł:
Implementation of MUSCL-Hancock method into the C++ code for the Euler equations
Autorzy:
Murawski, K.
Stpiczyński, P.
Powiązania:
https://bibliotekanauki.pl/articles/200996.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
hyperbolic equations
numerical methods
Godunow methods
Opis:
In this paper we present implementation of the MUSCL-Hancock method for numerical solutions of the Euler equations. As a result of the internal complexity of these equations solving them numerically is a formidable task. With the use of the original C++ code, we developed and presented results of a numerical test that was performed. This test shows that our code copes very well with this task.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 1; 45-53
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Godunov-type algorithms for numerical modeling of solar plasma
Autorzy:
Murawski, K.
Lee, D.
Powiązania:
https://bibliotekanauki.pl/articles/206269.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
computer science
modelling
numerical methods
hyperbolic equations
Opis:
We discuss numerical methods to solve the Cauchy problem for hyperbolic equations, paying attention to equations which describe physical phenomena in fluid dynamics. We concentrate on Godunov-type methods which adopt Riemann solvers. These methods constitute a formidable task due to complexity of hyperbolic equations. Despite this complexity we show that the Godunov-type methods can be successfully applied to simulate complex systems such as described by equations of magnetohydrodynamics. In particular, we simulate thermal mode in a two-dimensional x-point magnetic field topology that is embedded in a gravitationally stratified solar atmosphere.
Źródło:
Control and Cybernetics; 2012, 41, 1; 35-56
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
MPI-GPU/CUDA implementation of TVDLF method for the two-dimensional advection equation
Autorzy:
Murawski, K.
Stpiczyński, P.
Powiązania:
https://bibliotekanauki.pl/articles/206329.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
computer science
modelling
numerical methods
hyperbolic equations
Opis:
We implement Total Variation Diminishing Lax Friedrichs (TVDLF, or Rusanov) method to obtain numerical solutions of the two-dimensional advection equation. Despite the simplicity of this equation, solving it numerically is a formidable task. Based on the use of the original C++ MPI-GPU/CUDA code we present results of numerical tests we performed. These tests show that our code represents well the square wave profiles, leading to up to 60- times faster calculations with the use of MPI than with its serial counter-part.
Źródło:
Control and Cybernetics; 2014, 43, 2; 307-320
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation
Autorzy:
Lasiecka, I.
Triggiani, R.
Powiązania:
https://bibliotekanauki.pl/articles/970305.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
non-linear hyperbolic equations
uniform energy decay rates
Opis:
We consider the problem of uniform stabilization of nonlinear hyperbolic equations, epitomized by the following three canonical dynamics: (1) the wave equation in the natural state space L2(Ω) x H^-1(Ω), under nonlinear (and non-local) boundary dissipation in the Dirichlet B.C., as well as nonlinear internal damping; (2) a corresponding Kirchhoff equation in the natural state space [wzór), under nonlinear boundary dissipation in the 'moment' B.C. as well as nonlinear internal damping; (3) the system of dynamic elasticity corresponding to (1). All three dynamics possess a strong, hard-to-show 'boundary → boundary' regularity property, which was proved, also by invoking a micro-local argument, in Lasiecka and Triggiani (2004, 2008). This is by no means a general property of hyperbolic or hyperbolic-like dynamics (Lasiecka and Triggiani, 2003, 2008). The present paper, as a continuation of Lasiecka and Triggiani (2008), seeks to take advantage of this strong regularity property in the case of those PDE dynamics where it holds true. Thus, under the above boundary → boundary regularity, as well as exact controllability of the corresponding linear model, uniform stabilization of nonlinear models is obtained under minimal nonlinear assumptions, provided that a corresponding unique continuation property holds true. The treatment of the present paper is cast in the abstract setting (Lasiecka, 1989, 2001; Lasiecka and Triggiani, 2000, Ch. 7, 2003, 2008), which is proper for these hyperbolic dynamics and recovers the results of Lasiecka and Triggiani (2003, 2008) in the absence of the nonlinear interior damping, in particular in the linear case.
Źródło:
Control and Cybernetics; 2008, 37, 4; 935-969
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Godunov-type numerical methods for one- and two-component magnetohydrodynamic equations
Autorzy:
Murawski, K.
Powiązania:
https://bibliotekanauki.pl/articles/1943228.pdf
Data publikacji:
2009
Wydawca:
Politechnika Gdańska
Tematy:
numerical simulations of hyperbolic equations
Godunov methods
magnetohydrodynamics
Opis:
In this paper we review Godunov-type numerical methods for one- and two-component magnetohydrodynamic equations. Solving these equations numerically is a formidable task as a result of the internal complexity of these equations and the requirements of [delta] B=0. We present several results of advanced numerical simulations for complex systems. These results prove that the numerical codes which are based on Godunov-type methods, cope with all problems very well.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2009, 13, 1-2; 45-73
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH
Autorzy:
Murawski, K.
Lee, D.
Powiązania:
https://bibliotekanauki.pl/articles/202336.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
numerical methods for hyperbolic equations
finite volume method
Godunov-type methods
Opis:
In this paper we review numerical methods for hydrodynamic equations. Internal complexity make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system with a use of a publicly available code, FLASH. These results proof that the numerical methods cope very well with this task.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2011, 59, 1; 81-91
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical solutions of magnetohydrodynamic equations
Autorzy:
Murawski, K.
Powiązania:
https://bibliotekanauki.pl/articles/202271.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
numerical methods for hyperbolic equations
finite volume method
Godunov-type methods
magnetohydrodynamics
Opis:
In this paper we review several mathematical aspects in numerical methods for magnetohydrodynamic equations. The intrinsic complexity and the requirements of the selenoidity condition make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system, which reveal that the numerical methods cope very well with this task.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2011, 59, 2; 219-226
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The method of quasilinearization for system of hyperbolic functional differential equations
Autorzy:
Karpowicz, Adrian
Powiązania:
https://bibliotekanauki.pl/articles/745763.pdf
Data publikacji:
2008
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Monotone iterative technique
Generalized quasilinearization
Hyperbolic equations
Darboux problem
Functional differential inequalities
Opis:
We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations \[ \begin{cases} \frac{\partial^2 u}{\partial x\partial y} (x,y) = f(x,y,u_{(x,y)}, u_{(x,y)}, \text{a.e. in}\ [0,1]\times [0,b]\\ u(x,y) = \psi (x,y), \text{on}\ [-a_0,a]\times [-b_0,b] \setminus (0,a] \times (0,b], \end{cases} \] where the function \(u_{(x,y)}\colon [-a_0,0]\times [-b_0,0] \to \mathbb{R}^k\) is defined by \(u_{(x,y)} (s, t) = u(s + x, t + y)\) for \((s, t)\in [-a_0 , 0] \times [-b_0 , 0]\).
Źródło:
Commentationes Mathematicae; 2008, 48, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges
Autorzy:
Liu, Yang
Yang, Chao
Powiązania:
https://bibliotekanauki.pl/articles/2048892.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fourth-order nonlinear hyperbolic equations
weak solutions
exponential decay
family of potential wells
Opis:
This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.
Źródło:
Opuscula Mathematica; 2022, 42, 2; 239-255
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Autorzy:
Rencławowicz, Joanna
Zajączkowski, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1339037.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
relativistic hydrodynamics
symmetrization
existence
system of hyperbolic equations of the first order
initial-boundary value problem
Opis:
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 2; 221-252
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hyperbolicity of Systems Describing Value Functions in Differential Games which Model Duopoly Problems
Autorzy:
Zwierzchowska, J.
Powiązania:
https://bibliotekanauki.pl/articles/375973.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
duopoly models
semi-cooperative feedback strategies
Pareto optimality
hyperbolic partial differential equations
Opis:
Based on the Bressan and Shen approach (Bressan and Shen, 2004; Shen, 2009), we present an extension of the class of non-zero sum differential games for which value functions are described by a weakly hyperbolic Hamilton–Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly.
Źródło:
Decision Making in Manufacturing and Services; 2015, 9, 1; 89-100
1896-8325
2300-7087
Pojawia się w:
Decision Making in Manufacturing and Services
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient
Autorzy:
Farahani, H. S.
Telabi, H. A.
Baghermenhaj, M.
Powiązania:
https://bibliotekanauki.pl/articles/229317.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
drilling systems
adaptive control
hyperbolic partial differential equations
wave equation
boundary control
Opis:
The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.
Źródło:
Archives of Control Sciences; 2017, 27, 1; 63-76
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximate state-space and transfer function models for 2x2 linear hyperbolic systems with collocated boundary inputs
Autorzy:
Bartecki, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/330464.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
distributed parameter system
hyperbolic equations
approximation model
state space
transfer function
układ o parametrach rozłożonych
równanie hiperboliczne
model aproksymacyjny
przestrzeń stanu
funkcja przesyłowa
Opis:
Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 475-491
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Critical cases in neutral functional differential equations, arising from hydraulic engineering
Autorzy:
Răsvan, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/2216162.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
1D hyperbolic partial differential equations
neutral functional differential equation
difference operator
critical case
differential equations
Opis:
This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 605-633
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impulsive Hyperbolic System of Partial Differential Equations of Fractional Order with Delay
Autorzy:
Benchohra, Mouffak
Boutefal, Zohra
Powiązania:
https://bibliotekanauki.pl/articles/746465.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
impulsive partial hyperbolic differential equations,
fractional order, solution
left-sided mixed Riemann-Liouville integral
Caputo fractional-order derivative
finite delay
fixed point
Opis:
This paper deals with the existence of solutions to impulsive partial hyperbolic differential equations with finite delay, involving the Caputo fractional derivative. Our results will be obtained using Krasnoselskii fixed point theorem.
Źródło:
Commentationes Mathematicae; 2014, 54, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 21

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