Related papers: A positivity preserving convergent event based asy…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…
The work presented in this paper is related to the development of positivity preserving Discontinuous Galerkin (DG) methods for Boltzmann - Poisson (BP) computational models of electronic transport in semiconductors. We pose the Boltzmann…
We describe a simple and effective algorithm for solving Poisson's equation in the context of self-gravity within the DISPATCH astrophysical fluid framework. The algorithm leverages the fact that DISPATCH stores multiple time slices and…
In this work, we propose a positivity-preserving scheme for solving two-dimensional advection-diffusion equations including mixed derivative terms, in order to improve the accuracy of lower-order methods. The solution to these equations, in…
While constraints arise naturally in many physical models, their treatment in mathematical and numerical models varies widely, depending on the nature of the constraint and the availability of simulation tools to enforce it. In this paper,…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
In this paper we analyze a PDE system modelling (non-isothermal) phase transitions and damage phenomena in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no {\em small perturbation assumption} is…
The energy stable flux reconstruction (ESFR) method provides an efficient and flexible framework to devise high-order linearly stable numerical schemes which can achieve high levels of accuracy on unstructured grids. While superconvergent…
In this paper we propose an explicit and positivity preserving scheme for the mean reverting CEV model which converges in the mean square sense with convergence order $a(a-1/2)$.
We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the…
A fully discrete implicit scheme is proposed for the Swift-Hohenberg model, combining the third-order backward differentiation formula (BDF3) for the time discretization and the second-order finite difference scheme for the space…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
We develop a structure-preserving numerical discretization for the electrostatic Euler-Poisson equations with a constant magnetic field. The scheme preserves positivity of the density, positivity of the internal energy and a minimum…
We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems. The BFECC method has been applied to schemes for advection equations to improve their stability and order of accuracy. Similar…
Event cameras are bio-inspired sensors that respond to per-pixel brightness changes in the form of asynchronous and sparse "events". Recently, pattern recognition algorithms, such as learning-based methods, have made significant progress…
For the first time, a general two-parameter family of entropy conservative numerical fluxes for the shallow water equations is developed and investigated. These are adapted to a varying bottom topography in a well-balanced way, i.e.…
An important class of problems exhibits macroscopically smooth behaviour in space and time, while only a microscopic evolution law is known. For such time-dependent multi-scale problems, the gap-tooth scheme has recently been proposed. The…