Related papers: A Nonlinear Projection-Based Iteration Scheme with…
In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to…
We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering.…
We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and Bhatnagar-Gross-Krook (BGK) equations. The methods employ a sequence of small forward-Euler steps,…
Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first…
We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption and scattering in many relevant societal applications, and requires numerical approximations. However,…
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…
The standard nonlocal thermodynamic equilibrium (non-LTE) multi-level radiative transfer problem only takes into account the deviation of the radiation field and atomic populations from their equilibrium distribution. We aim to show how to…
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the…
A new iterative method for non-LTE multilevel polarized radiative transfer in hydrogen lines is presented. Iterative methods (such as the Jacobi method) tend to damp out high-frequency components of the error fast, but converges poorly due…
This paper proposes and analyzes an implicit-explicit BDF-Galerkin scheme of second order for the time-dependent nonlinear thermistor problem. For this, we combine the second-order backward differentiation formula with special extrapolation…
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D…
We consider the iterative solution of anisotropic radiative transfer problems using residual minimization over suitable subspaces. We show convergence of the resulting iteration using Hilbert space norms, which allows us to obtain…
Accurately capturing and simulating multiscale systems is a formidable challenge, as both spatial and temporal scales can span many orders of magnitude. Rigorous upscaling methods not only ensure efficient computation, but also maintains…
We present a novel approach for solving the time-dependent Schr\"{o}dinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand…
The Reynolds-Averaged Navier-Stokes equations and the Large-Eddy Simulation equations can be coupled using a transition function to switch from a set of equations applied in some areas of a domain to the other set in the other part of the…