Related papers: Multigrid Methods for Polarized Radiative Transfer
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
We discuss the electromagnetic scattering and radiation problems of multilayered spheres, reviewing the history of the Lorentz-Mie theory and the numerical stability issues encountered in handling multilayered spheres. By combining…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium, taking…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
A multi-timescale hybrid model is proposed to study microscopically the degraded performance of electronic devices, covering three individual stages of radiation effects studies, including ultrafast displacement cascade, intermediate defect…
The Transfer Matrix Method is a powerful numerical tool for simulating wave propagation in layered media. It has been widely applied in many fields, although its use is typically restricted to passive media. In this paper, we develop the…
Non-LTE radiative transfer is a key tool for modern astrophysics: it is the means by which many key synthetic observables are produced, thus connecting simulations and observations. Radiative transfer models also inform our understanding of…
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…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
We present a new numerical approach that is able to solve the multi-dimensional radiative transfer equations in all opacity regimes on a Lagrangian, unstructured network of characteristics based on a stochastic point process. Our method…
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…
Extremely large-scale multiple-input-multipleoutput (XL-MIMO) has been reviewed as a promising technology for future sixth-generation (6G) networks to achieve higher performance. In practice, various linear precoding schemes, such as…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to…
Context: Radiative transfer modelling of expanding stellar envelopes is an important task in their analysis. To account for inhomogeneities and deviations from spherical symmetry, it is necessary to develop a 3D approach to radiative…
We are interested in numerically solving the Hamilton-Jacobi (HJ) equations, which arise in optimal control and many other applications. Oftentimes, such equations are posed in high dimensions, and this poses great numerical challenges.…
Electromagnetic linear-to-circular polarization converters with wide- and multi-band capabilities can simplify antenna systems where circular polarization is required. Multi-band solutions are attractive in satellite communication systems,…