Temat: semi-Lagrangian method - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

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

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