Related papers: Advances in the Implementation of the Exactly Ener…
Particle-in-Cell (PIC) methods employ particle representations of unknown fields, but also employ continuum fields for other parts of the problem. Thus projection between particle and continuum bases is required. Moreover, we often need to…
Due to reduced manufacturing yields, traditional monolithic chips cannot keep up with the compute, memory, and communication demands of data-intensive applications, such as rapidly growing deep neural network (DNN) models. Chiplet-based…
We review common extensions of particle-in-cell (PIC) schemes which account for strong field phenomena in laser-plasma interactions. After describing the physical processes of interest and their numerical implementation, we provide…
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau…
The single particle model (SPM) is a reduced electrochemical model that holds promise for applications in battery management systems due to its ability to accurately capture battery dynamics; however, the numerical discretization of the SPM…
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this…
Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here…
We describe the remapped particle-mesh method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In…
Native extracellular matrices (ECMs), such as those of the human brain and other neural tissues, exhibit networks of molecular interactions between specific matrix proteins and other tissue components. Guided by these naturally…
Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via…
We introduce a simplified model of the electron-beam/plasma system to model the electrical breakdown caused by the inductive electric field created by a rapidly rising electron beam current. The rigid-beam model is a reduction to the…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
Particle-in-Cell (PIC) methods are widely used computational tools for fluid and kinetic plasma modeling. While both the fluid and kinetic PIC approaches have been successfully used to target either kinetic or fluid simulations, little was…
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…
The Particle-In-Cell (PIC) method for plasma simulation tracks particle phase space information using particle and grid data structures. High computational costs in 2D and 3D device-scale PIC simulations necessitate parallelization, with…
The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum…
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $\gamma(\theta)$ -- anisotropic surface diffusion -- in two…
Tackling climate change requires the rapid and deep decarbonization of electric power systems. While energy management systems (EMSs) play a central role in this transition, conventional EMSs focus mainly on economic efficiency and often…
Smoothing short-wavelength charge density variations can stabilize explicit electrostatic particle-in-cell (PIC) plasma simulations against grid heating and cold beam instabilities, which cause unphysical heating when the Debye length is…
In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining…