Related papers: Multigrid Methods for Polarized Radiative Transfer
The propagation of s- and p-polarized light through quasiperiodic multilayers, consisting of layers with different refractive indices, is studied by the transfer matrix method. In particular, we focus on the transmission coefficient of the…
Thermal radiative transfer (TRT) presents significant computational challenges due to the stiff, nonlinear coupling between radiation and material energy, particularly in multigroup, high-fidelity transport models. In this work, we develop…
We consider waveform iterations for dynamical coupled problems, or more specifically, PDEs that interact through a lower dimensional interface. We want to allow for the reuse of existing codes for the subproblems, called a partitioned…
We present a metriplectic formulation of the radiative transfer equation with polarization and varying refractive index and show that this formulation automatically satisfies the first two laws of thermodynamics. In particular, the derived…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…
This paper establishes the iteration-complexity of a Jacobi-type non-Euclidean proximal alternating direction method of multipliers (ADMM) for solving multi-block linearly constrained nonconvex programs. The subproblems of this ADMM variant…
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…
We present a hierarchical approach for enhancing the robustness of numerical solvers for modelling radiative MHD flows in multi-dimensions. This approach is based on clustering the entries of the global Jacobian in a hierarchical manner…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.…
Transfer matrix method is a well-known and extensively used tool to compute the reflection and transmission coefficients of electromagnetic waves when interacting with a system of layers parallel to each other. We present here a modified…
Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
By means of the transfer matrix method, the optical properties of fibers with a distinct intermediate layer between a hol-low core and periodic cladding are calculated. The periodic cladding consists of two types of the alternating layers.…