相关论文: Gauss collocation methods for efficient structure …
Most physical processes posses structural properties such as constant energies, volumes, and other invariants over time. When learning models of such dynamical systems, it is critical to respect these invariants to ensure accurate…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…
In this paper we study the geometric solution of the so called "good" Boussinesq equation. This goal is achieved by using a convenient space semi-discretization, able to preserve the corresponding Hamiltonian structure, then using…
In this paper, we propose the diagonal implicit Runge-Kutta methods and transformed Runge-Kutta methods for stochastic Poisson systems with multiple noises. We prove that the first methods can preserve the Poisson structure, Casimir…
An approach is treated for numerical integration of ordinary differential equations systems of the first order with choice of a computation scheme, ensuring the required local precision. The treatment is made on the basis of schemes of…
In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system coupled with Poisson or Amp\`ere equation. Splitting methods…
Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
The present work deals with an improved back-propagation algorithm based on Gauss-Newton numerical optimization method for fast convergence. The steepest descent method is used for the back-propagation. The algorithm is tested using various…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
Hessian information speeds convergence substantially in motion optimization. The better the Hessian approximation the better the convergence. But how good is a given approximation theoretically? How much are we losing? This paper addresses…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
We consider the efficient numerical solution of coupled dynamical systems, consisting of a small nonlinear part and a large linear time invariant part, possibly stemming from spatial discretization of an underlying partial differential…
We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
An explicit second-order numerical method to integrate the isokinetic equations of motion is derived by fitting circular arcs through every three consecutive points of the discretized trajectory, so that the tangent and the curvature…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…