Related papers: A variational symplectic scheme based on Lobatto's…
In this paper we present splitting methods which are based on iterative schemes and applied to stochastic nonlinear Schroedinger equation. We will design stochastic integrators which almost conserve the symplectic structure. The idea is…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
A basic leapfrog integrator and its energy-preserving and variational / symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than…
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…
Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical methods.…
Recently, an extended version of magnetohydrodynamics that incorporates electron inertia, dubbed inertial magnetohydrodynamics, has been proposed. This model features a noncanonical Hamiltonian formulation with a number of conserved…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
A novel implicit integration scheme for the Discrete Element Method (DEM) based on the variational integrator approach is presented. The numerical solver provides a fully dynamical description that, notably, reduces to an energy…
Recently, a whole class of evergy-preserving integrators has been derived for the numerical solution of Hamiltonian problems. In the mainstream of this research, we have defined a new family of symplectic integrators depending on a real…
We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
The choice of a time integration scheme is a crucial aspect of any transient fluid simulation, and Smoothed-Particle Hydrodynamics (SPH) is no exception. The influence of the time integration scheme on energy balance is here addressed. To…
Geometric integrators of the Schr\"{o}dinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement, but, unfortunately, is restricted to…
We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend…
Efficient fourth order symplectic integrators are proposed for numerical integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric splitting coefficients with five to nine stages are obtained by higher order decomposition of…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…