Related papers: Multigroup Neutron Transport using a Collision-Bas…
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…
Within the mode-coupling theory (MCT) of the glass transition, we reconsider the numerical schemes to evaluate the MCT functional. Here we propose nonuniform discretizations of the wave number, in contrast to the standard equidistant grid,…
We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…
The nucleon spectral function in infinite nuclear matter is calculated in a quantum transport theoretical approach. Exploiting the known relation between collision rates and correlation functions the spectral function is derived…
The unified gas-kinetic wave-particle (UGKWP) method is proposed for the neutron transport equation, addressing the inherent multiscale nature of neutron propagation in both optically thin and thick regimes. UGKWP couples macroscopic…
We apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator.…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
Collisional fragmentation is a ubiquitous phenomenon arising in a variety of astrophysical systems, from asteroid belts to debris and protoplanetary disks. Numerical studies of fragmentation typically rely on discretizing the size…
Background: A quantitative microscopic understanding of the fission-fragment yield distributions represents a major challenge for nuclear theory as it involves the intricate competition between large-amplitude nuclear collective motion and…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…
Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging…
This paper presents hybrid numerical techniques for solving the Boltzmann transport equation formulated by means of low-order equations for angular moments of the angular flux. The moment equations are derived by the projection operator…
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…
We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…