Related papers: An entropic fourier method for the Boltzmann equat…
This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…
In this work, we propose a new Galerkin-Petrov method for the numerical solution of the classical spatially homogeneous Boltzmann equation. This method is based on an approximation of the distribution function by associated Laguerre…
Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce…
We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random $N$-vectors. We achieve this by deducing a specific integral representation for the Hessian matrix of a solution…
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite…
We present a tensor-decomposition method to solve the Boltzmann transport equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method represents the six-dimensional BTE as a set of six one-dimensional problems, which are solved…
We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability distributions can be extended to discrete probability…
We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and,…
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…
In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
An elegant and uniform relaxation-rate formula is presented for the entropic lattice Boltzmann method (ELBM). The formula not only guarantees the discrete time H-theorem at numerical level but also gives full consideration to the…
We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty…
In this paper, we develop a Bernstein dual-Petrov-Galerkin method for the numerical simulation of a two-dimensional fractional diffusion equation. A spectral discretization is applied by introducing suitable combinations of dual Bernstein…
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to…
We numerically solve the Boltzmann equation for trapped fermions in the normal phase using the test-particle method. After discussing a couple of tests in order to estimate the reliability of the method, we apply it to the description of…
An operator-splitting finite element scheme for the time-dependent, high-dimensional radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite…