An averaging technique for highly-oscillatory Hamiltonian problems

International audienceIn this paper, we are concerned with the numerical solution of highly-oscillatory Hamiltonian systems with a stiff linear part. We construct an averaged system whose solution remains close to the exact one over bounded time intervals, possesses the same adiabatic and Hamiltonian invariants as the original system, and is non-stiff. We then investigate its numerical approximation through a method which combines a symplectic integration scheme and an acceleration technique for the evaluation of time-averages developped in a previous paper. Eventually, we demonstrate the efficiency of our approach on two test problems with one or several frequencies

Long-time averaging for integrable Hamiltonian dynamics

International audienceGiven a Hamiltonian dynamics, we address the question of computing the space-average (referred as the ensemble average in the field of molecular simulation) of an observable through the limit of its time-average. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that the two averages then coincide. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a numerical symplectic scheme is applied to the system, up to the order of the integrator

High-order averaging schemes with error bounds for thermodynamical properties calculations by MD simulations

We introduce high-order averaging formulae for the computation of statistical averages on the basis of the numerical simulation of long-time molecular dynamics trajectories. Using these formulae, we improve the convergence rate of the time average with respect to the computational effort. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give error bounds that provide guidelines to choose the parameters of the computation in order to reach a given desired accuracy in the most efficient manner

Trégor-Goëllo (Côtes-dArmor). Châteaux forts et habitats seigneuriaux fortifiés en pierre

Chartier Erwan. Trégor-Goëllo (Côtes-dArmor). Châteaux forts et habitats seigneuriaux fortifiés en pierre. In: Archéologie médiévale, tome 27, 1997. pp. 253-254