Related papers: An exponential integrator for a highly oscillatory…
The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation,…
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the…
The one-dimensional Vlasov-Poisson system is considered and a particle method is developed to approximate solutions without compact support which tend to a fixed background of charge as $| x | \to \infty$. Such a system of equations can be…
We propose and study a Particle-In-Cell (PIC) method based on the Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of…
The Vlasov-Poisson system, modeling the evolution of non-collisional plasmas in the electrostatic limit, is approx- imated by a Semi-Lagrangian technique. Spectral methods of periodic type are implemented through a collocation approach.…
We extend the recently developed entropic and conservative variance reduction framework [M. Sadr, N. G. Hadjiconstantinou, A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…
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 machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
It is known in \cite{beccari} that the standard explicit Euler-type scheme (such as the exponential Euler and the linear-implicit Euler schemes) with a uniform timestep, though computationally efficient, may diverge for the stochastic…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…
Traditional step size controllers make the tacit assumption that the cost of a time step is independent of the step size. This is reasonable for explicit and implicit integrators that use direct solvers. In the context of exponential…
We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
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…
Outstanding advances in solid-state laser technology, employing the optical parametric chirped-pulse-amplification (OPCPA) technique, have led physicists to focus laser pulses to highly-relativistic intensities which led to novel schemes…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
Particle methods are a ubiquitous tool for solving the Vlasov-Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter in an expanding universe. However, these methods are known to produce…