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    Wyświetlanie 1-4 z 4
    Tytuł:
    Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation
    Autorzy:
    Crouseilles, N.
    Latu, G.
    Sonnendrücker, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/929688.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Vlasova-Poissona
    metoda Lagrangiana
    równoległość
    Vlasov-Poisson equation
    semi-Lagrangian method
    parallelism
    Opis:
    This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle- In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being devoted to a processor. Some Hermite boundary conditions allow for the reconstruction of a good approximation of the global solution. Several numerical results demonstrate the accuracy and the good scalability of the method with up to 64 processors. This work is a part of the CALVI project.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 335-349
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena
    Autorzy:
    Besse, N.
    Mauser, N. J.
    Sonnendrücker, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/929699.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    model Vlasova-Darwina
    model Vlasova-Poiswell'a
    metoda Lagrangiana
    niskoczęstotliwościowe zjawisko elektromagnetyczne
    Vlasov-Darwin model
    Vlasov-Poisswell model
    semi-Lagrangian method
    low-frequency electromagnetic
    Opis:
    We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus “light waves” are somewhat supressed, which in turn allows the numerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian methods and time splitting techniques. We develop a four-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two-dimensional Cartesian grid. Finally, we present two nontrivial test cases: (a) the wave Landau damping and (b) the electromagnetic beam-plasma instability. For these cases our numerical scheme works very well and is in agreement with analytic kinetic theory.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 361-374
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation
    Autorzy:
    Campos Pinto, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/929689.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda Lagrangiana
    oszacowanie błędu
    szybkość zbieżności
    fully adaptive scheme
    semi-Lagrangian method
    Vlasov-Poisson equation
    error estimate
    convergence rates
    optimal transport of adaptive multiscale meshes
    Opis:
    This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1 + 1)- dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport multiscale meshes along a smooth flow, in a way that can be said optimal in the sense that it satisfies both accuracy and complexity estimates which are likely to lead to optimal convergence rates for the whole numerical scheme. From the regularity analysis of the numerical solution and how it gets transported by the numerical flow, it is shown that the accuracy of our scheme is monitored by a prescribed tolerance parameter \epsilon which represents the local interpolation error at each time step. As a consequence, the numerical solutions are proved to converge in L\infty towards the exact ones as \epsilon and \delta t tend to zero, and in addition to the numerical tests presented in (Campos Pinto and Mehrenberger, 2007), some complexity bounds are established which are likely to prove the optimality of the meshes.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 351-359
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
    Autorzy:
    Barboteu, M.
    Bartosz, K.
    Kalita, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/330898.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    linearly elastic material
    bilateral contact
    nonmonotone friction law
    hemivariational inequality
    finite element method
    error estimate
    nonconvex proximal bundle method
    quasi augmented Lagrangian method
    Newton method
    metoda elementów skończonych
    szacowanie błędu
    metoda Lagrangiana
    metoda Newtona
    Opis:
    We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 263-276
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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