Related papers: Monte Carlo stochastic Galerkin methods for the Bo…
The claim that Monte Carlo is the most accurate method is a case of misattributed credit. This claim is based on experience with advanced systems MCNPX, Geant4 and EGS. These systems achieve remarkable performance because they use most…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain…
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…
This paper presents a perspective in which Direct Simulation Monte Carlo (DSMC) is viewed not in its traditional role as an algorithm for solving the Boltzmann equation but as a numerical method for statistical mechanics. First, analytical…
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic…
We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly…
We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation…
This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure…
Understanding fundamental kinetic processes is important for many problems, from plasma physics to gas dynamics. A first-principles approach to these problems requires a statistical description via the Boltzmann equation, coupled to…
One- and multi-dimensional stochastic Maxwell equations with additive noise are considered in this paper. It is known that such system can be written in the multi-symplectic structure, and the stochastic energy increases linearly in time.…
We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced…
With the rapid advancement of information technology and data collection systems, large-scale spatial panel data presents new methodological and computational challenges. This paper introduces a dynamic spatial panel quantile model that…
We introduce numerical solvers for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. Due to the quadratic collision operator in the Boltzmann equation, the SGS method requires solving a nonlinear system…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…