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    Wyświetlanie 1-4 z 4
    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:
    Sequential optimization for semilinear divergent hyperbolic equation with a boundary control and state inequality constraint
    Autorzy:
    Gavrilov, V. S.
    Sumin, M. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/206311.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Radon measures
    sequential optimization
    maximum principle for minimizing sequences
    semilinear hyperbolic partial differential equations
    pointwise in time state constraints
    boundary control
    value function
    sensitivity
    normality
    regularity
    twoparameter needle variation of controls
    Opis:
    An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.
    Źródło:
    Control and Cybernetics; 2014, 43, 2; 183-226
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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