相关论文: Solving the Discretised Boltzmann Transport Equati…

One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…

This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical…

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard…

We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…

While the Boltzmann transport equation can accurately model transport problems with highly forward-peaked scattering, obtaining its solution can become arbitrarily slow due to near-unity spectral radius associated with source iteration.…

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…

This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…

The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…

The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric…

This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…

In this study a spatio-temporal approach for the solution of the time-dependent Boltzmann (transport) equation is derived. Finding the exact solution using the Boltzmann equation for the general case is generally an open problem and…

We have coded a Boltzmann solver based on a finite difference scheme (S_N method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been…

Heterogeneous computing environments combining CPU and GPU resources provide a great boost to large-scale scientific computing applications. Code generation utilities that partition the work into CPU and GPU tasks while considering data…

In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…

This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically…

With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium…

In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…

Discontinuous Finite Element Methods (DFEM) have been widely used for solving $S_n$ radiation transport problems in participative and non-participative media. In the DFEM $S_n$ methodology, the transport equation is discretized into a set…

We introduce a new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae. Our algorithm avoids the need to spell out the complicated advection terms in energy…