Related papers: Efficient energy-preserving methods for charged-pa…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the…
Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order conditions are simplified and parallelizable conditions are…
We discuss the interpolation of the electric and magnetic fields within a charge-conserving Particle-In-Cell scheme. The choice of the interpolation procedure for the fields acting on a particle can be constrained by analyzing conservation…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
During a crossover via a switching mechanism from one 2-body potential to another as might be applied in modeling (chemical) reactions in the vicinity of bond formation, energy violations would occur due to finite step size which determines…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
The computational bottleneck of molecular dynamics is the pairwise additive long-range interactions between particles. The random batch Ewald (RBE) method provides a highly efficient and superscalable solver for long-range interactions, but…
We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of any large systems of algebraic equations). In space, we use…
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…
In this paper, we define arbitrarily high-order energy-conserving methods for Hamiltonian systems with quadratic holonomic constraints. The derivation of the methods is made within the so-called line integral framework. Numerical tests to…
Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce…
In this paper, we present a novel class of high-order energy-preserving schemes for solving the Zakharov-Rubenchik equations. The main idea of the scheme is first to introduce an quadratic auxiliary variable to transform the Hamiltonian…
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling…
Grid-connected hybrid renewable power systems with energy storage can reduce the intermittency of renewable power supply. However, emerging energy storage technologies need improvement to compete with lithium-ion batteries and reduce the…
An implementation of an electron temperature-dependent interaction potential for copper in a two-temperature model-molecular dynamics framework is presented. An algorithm for enforcing energy conservation when using such an interaction is…
In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the…
We consider the issue of strict, fully discrete \emph{local} energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms…