Aims. We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number of physical problems than Cartesian coordinates. Methods. The scattering problem for line transfer is solved via means of an operator splitting (OS) te...

While it is possible to numerically evolve the relativistic fluid equations using any chosen coordinate mesh, typically there are distinct computational advantages associated with different types of candidate grids. For example, astrophysical flows that are governed by rotation tend to give rise to advection variables that are naturally conserved when a cylindrical mesh is used. On the other ha...

Artificially structured metamaterials have enabled unprecedented flexibility in manipulating electromagnetic waves and producing new functionalities, including the cloak of invisibility based on coordinate transformation. Unlike other cloaking approaches4–6, which are typically limited to subwavelength objects, the transformation method allows the design of cloaking devices that render a macros...

The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domai...

We present discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and a generalized higher-order moment equation of the Boltzmann transport equation for general orthogonal coordinate systems like cylindrical and spherical systems. The use of orthogonal coordinate systems allows to reduce the dimension of the problem from three to two. We give an approximation...

This paper consists of three sections. In the first section an efficient method is used for decomposition of the canonical matrices associated with repetitive structures. to this end, cylindrical coordinate system, as well as a special numbering scheme were employed. In the second section, divide and conquer method have been used for eigensolution of these structures, where the matrices are in ...