Related papers: High-order exponential solver method for particle-…
In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…
In this article we describe a unifying framework for variational electromagnetic particle schemes of spectral type, and we propose a novel spectral Particle-In-Cell (PIC) scheme that preserves a discrete Hamiltonian structure. Our work is…
An efficient numerical algorithm for the laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We develop a numerical scheme for solving time-domain Maxwell's equation. The method is motivated by CIP method which uses function values and its derivatives as unknown variables. The proposed scheme is developed by using the Poisson…
Coulomb collisions in particle simulations for weakly coupled plasmas are modeled by the Landau-Fokker-Planck equation, which is typically solved by Monte-Carlo (MC) methods. One of the main disadvantages of MC is the timestep accuracy…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on…
This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…
We use Bayesian optimization in combination with three-dimensional particle-in-cell simulations to determine the optimal laser and plasma parameters that, for a given laser pulse energy, maximize the cut-off energy of an electron beam…
Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…
Large-scale simulations of plasmas are essential for advancing our understanding of fusion devices, space, and astrophysical systems. Particle-in-Cell (PIC) codes have demonstrated their success in simulating numerous plasma phenomena on…
In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for Maxwell equations in Cole-Cole…
Until recently, electromagnetic finite element PIC (EM-FEMPIC) methods that demonstrated charge conservation used explicit field solvers. It is only recently, that a series of papers developed the mathematics necessary for charge…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…
We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple…