Related papers: Alternating-Order Interpolation in a Charge-Conser…
In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step…
We present the standard electromagnetic Particle-in-Cell method, starting from the discrete approximation of derivatives on a uniform grid. The application to second-order, centered, finite-difference discretization of the equations of…
We study the charge ordering behavior under a magnetic field $H$ in the extended Hubbard model within the coherent potential approximation. At quarter filling, for small $H$ we find that the relative variation of critical temperature is…
Particle-In-Cell codes are widely used for plasma physics simulations. It is often the case that particles within a computational cell need to be split to improve the statistics or, in the case of non-uniform meshes, to avoid the…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric…
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of…
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…
Energy conserving particle-in-cell schemes are constructed for a class of reduced relativistic Vlasov--Maxwell equations of laser-plasma interaction. Discrete Poisson equation is also satisfied by the numerical solution. Specifically,…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an…
We analyze the structure of higher-order radiative corrections for processes with unstable particles. By subsequently integrating out the various scales that are induced by the presence of unstable particles we obtain a hierarchy of…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
We present a phenomenological model for magnetoelectricity in multiferroic materials. The distinctive feature of the model is a two-component complex order parameter that encodes the electric polarization, along with a direct coupling…
Modeling of kinetic plasmas using electromagnetic particle in cell methods (EM-PIC) is a problem that is well worn, in that methods developed have been used extensively both understanding physics and exploiting them for device design.…