On the rate of convergence of the Hamiltonian particle-mesh method
نویسندگان
چکیده
The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numerical short-time study of the rate of convergence of HPM in terms of its three main governing parameters. We find that the rate of convergence is much better than the best available theoretical estimates. Our results indicate that HPM performs best when the number of particles is on the order of the number of grid cells, the HPM global smoothing kernel has fast decay in Fourier space, and the HPM local interpolation kernel is a cubic spline.
منابع مشابه
Convergence of the Hamiltonian particle-mesh method for barotropic fluid flow
We prove convergence of the Hamiltonian Particle-Mesh (HPM) method, initially proposed by J. Frank, G. Gottwald, and S. Reich, on a periodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible fluid flow. Under appropriate assumptions, most notably sufficiently fast decay in Fourier space of the global smoothing operator, and a Str...
متن کاملConvergence Rate for a Radau Hp Collocation Method Applied to Constrained Optimal Control ∗
Abstract. For control problems with control constraints, a local convergence rate is established for an hp-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighb...
متن کاملPareto-optimal Solutions for Multi-objective Optimal Control Problems using Hybrid IWO/PSO Algorithm
Heuristic optimization provides a robust and efficient approach for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. The convergence rate and suitable diversity of solutions are of great importance for multi-objective evolutionary algorithms. The focu...
متن کاملHamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation
We develop a particle-mesh method for two-layer shallow-water equations subject to the rigid-lid approximation. The method is based on the recently proposed Hamiltonian particle-mesh (HPM) method and the interpretation of the rigid-lid approximation as a set of holonomic constraints. The suggested spatial discretization leads to a constrained Hamiltonian system of ODEs which is integrated in ti...
متن کاملThe Hamiltonian particle-mesh method for the spherical shallow water equations
The Hamiltonian particle-mesh (HPM) method is generalized to the spherical shallow water equations, utilizing constrained particle dynamics on the sphere and smoothing with Merilees’ double-periodic FFT formulation of O(J log J) in the latitudinal gridsize. The time step for the explicit, symplectic integrator depends only on the uniform smoothing length. 2000 Mathematics Subject Classification...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012