相关论文: A new computational framework for particle and spi…

Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein--Euler equations of general relativity based on a first order…

A fully discrete Galerkin scheme for a thermodynamically consistent transient Max-well-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the…

This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

In this paper we present a new technique for efficiently implementing Large Eddy Simulation with the Discontin- uous Galerkin method on unstructured meshes. In particular, we will focus upon the approach to overcome the computational…

A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…

Deterministic solutions of the Boltzmann equation represent a real challenge due to the enormous computational effort which is required to produce such simulations and often stochastic methods such as Direct Simulation Monte Carlo (DSMC)…

In this paper, we consider the numerical solution of the one-dimensional Schr\"odinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness is…

Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptive Galerkin FE method for linear parametric PDEs with…

We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. These schemes are designed to be systematically as accurate…

In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koornwinder polynomials are introduced on the reference…

The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…

We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of…

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…

In recent work it is shown that importance sampling can be avoided in the particle filter through an innovation structure inspired by traditional nonlinear filtering combined with Mean-Field Game formalisms. The resulting feedback particle…

We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singu- lar nature of the solution, the standard gPC-SG methods may suffer from a poor or…

A novel approach for the stabilization of the discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. The approach is centered around the efficient solution of linear or nonlinear optimization problems in…

We elaborate on the methodology to simulate bulk systems in the absence of time-reversal symmetry by the phase-fixed path-integral Monte Carlo method under (possibly twisted) periodic boundary conditions. Such systems include…

We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…