Related papers: Filtered Hyperbolic Moment Method for the Vlasov E…
This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-preserving (BP) limitings, which is an extension of our…
This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…
In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…
The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in…
A method of solution of the collisionless Vlasov equation, by following collisionless phase point trajectories in phase space, is presented. It is shown that by increasing the number of phase points, without enhancing the resolution of…
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. All approaches have a direct analogy to existing and…
When simulating hyperbolic conservation laws with discontinuous solutions, high-order linear numerical schemes often produce undesirable spurious oscillations. In this paper, we propose a jump filter within the discontinuous Galerkin (DG)…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
We consider a second order non-autonomous system which can be interpreted as the Newtonian equation of motion on a Riemannian manifold under the action of time-quasiperiodic force field. The problem is to find conditions which ensures: (a)…
Parametric rolling is one of the dangerous dynamic phenomena. In order to discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect…
We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are…
We study the task of learning latent-variable models. A common algorithmic technique for this task is the method of moments. Unfortunately, moment-based approaches are hampered by the fact that the moment tensors of super-constant degree…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain.…
This short note presents an extension of the hybrid, model-adaptation method introduced in [T.~Laidin, \textit{arXiv 2202.03696}, 2022] for linear collisional kinetic equations in a diffusive scaling to the nonlinear mean-field…
A nonlinear kinetic equation for nonrelativistic quantum plasma with electromagnetic interaction of particles is obtained in the Hartree's mean-field approximation. It is cast in a convenient form of Vlasov-Boltzmann-type equation with…
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…
The present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time…
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - in order to compute, both, entropy dissipative solutions…
We present a class of hybrid FD-FV (finite difference and finite volume) methods for solving general hyperbolic conservation laws written in first-order form. The presentation focuses on one- and two-dimensional Cartesian grids; however,…