Related papers: Adding an energy-like conservation law to the leap…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…
In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum…
We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird…
I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such…
We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the…
The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To partially eliminate these…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct…
Ionic electro-active polymer (Nafion for example) can be used as sensor or actuator. To this end, a thin film of the water-saturated material is sandwiched between two electrodes. Water saturation causes a quasi-complete dissociation of the…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One promising strategy to improve their energy economy is to leverage their natural…
Time-centered, hence second-order, methods for integrating the relativistic momentum of charged particles in an electromagnetic field are derived. A new method is found by averaging the momentum before use in the magnetic rotation term, and…
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…