相关论文: Exact local conservation of energy in fully implic…

In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38(2016) A1876-A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea…

Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not…

In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry.…

We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator…

In this work, we present a novel family of explicit relaxation Particle-in-Cell (ER-PIC) methods for the Vlasov-Poisson equation with a strong magnetic field. These schemes achieve exact energy conservation by combining a splitting…

Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…

We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…

We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…

We present a new technique for transferring momentum and velocity between particles and grid with Particle-In-Cell (PIC) calculations which we call Affine-Particle-In-Cell (APIC). APIC represents particle velocities as locally affine,…

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that…

Particle-in-cell (PIC) plasma simulations are a productive and valued tool for the study of nonlinear plasma phenomena, yet there are basic questions about the simulation methods themselves that remain unanswered. Here we study one such…

We present a fully variational locally scaled self-interaction corrected (SIC) energy functional using complex optimal orbitals. This represents an important milestone for fully variational SIC energy functionals, which have been shown to…

This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…

We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of…

We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…

A recent paper by Huang et al. [Computer Physics Communications 207, 123 (2016)] thoroughly analyzed the Finite Grid Instability(FGI) and spectral fidelity of standard Particle-In-Cell (PIC) methods. Numerical experiments were carried out…