Related papers: A particle micro-macro decomposition based numeric…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
In the present work, a novel particle merging scheme is proposed for PIC-DSMC simulations, based on the solution of a Non-negative Least Squares problem. The merging algorithm conserves arbitrary moments of the velocity distribution…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
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…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of inter-particle interactions are taken into account: (1) long- and (2) short-range…
Systematic deflection of microparticles off of initial streamlines is a fundamental task in microfluidics, aiming at applications including sorting, accumulation, or capture of the transported particles. In a large class of setups,…
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…
Recent advances in random-walk particle-tracking have enabled direct simulation of mixing and reactions on particles by allowing the particles to interact with each other using a multi-point mass transfer scheme. The mass transfer scheme…
This article is concerned with the development of a theoretical framework of global measure-valued solutions for a class of hyperbolic-parabolic cross-diffusion systems, and its application to the convergence analysis of a fully discrete…
In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element discretization for the macroscopic fluid dynamic equation with a deterministic variational particle…