Related papers: Metriplectic particle-in-cell integrators for the …
We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…
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…
We discuss a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis. We describe a semi-implicit time discretization that extends the range of numerical…
In this paper, we present different types of integrators for electro-magnetic particle-in-cell (PIC) methods. While the integrator is an important tool of the PIC methods, it is necessary to characterize the different conservation…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated…
A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…
The aim of this paper is to introduce several new particle representations for \textit{ergodic} McKean-Vlasov SDEs. We construct new algorithms by leveraging recent progress in weak convergence analysis of interacting particle system. We…
We propose and analyze a non-iterative domain decomposition integrator for the linear acoustic wave equation. The core idea is to combine an implicit Crank-Nicolson step on spatial subdomains with a local prediction step at the subdomain…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
We are interested in the inhomogeneous Landau equation which describes the evolution of a particle density f = f (t, x, v) representing at time t $\ge$ 0, the density of particles at position x $\in$ R 3 and velocity v $\in$ R 3. The study…
We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…
We introduce the consecutive lifting-projection (LP) flow as a novel approximation framework for the spatially homogeneous Boltzmann and Landau equations. The key idea is to lift the nonlinear collision operator to a higher dimensional…
This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma…
We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include…
We consider a system of N particles interacting via a short-range smooth potential, in a intermediate regime between the weak-coupling and the low-density. We provide a rigorous derivation of the Linear Landau equation from this particle…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
In this paper, we extend the geometric Particle in Cell framework on dual grids to a gauge-free drift-kinetic Vlasov--Maxwell model and its coupling with the fully kinetic model. We derive a discrete action principle on dual grids for our…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…