Related papers: Some extensions of the $\phi$-divergence moment cl…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…
In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside…
To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson-Nernst-Planck(PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, which is second-order accurate in…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…