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Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
The sizable linear polarization signals produced by the scattering of anisotropic radiation in the core of the Ca I 4227 $\mathrm{\r{A}}$ line constitute an important observable for probing the inhomogeneous and dynamic plasma of the lower…
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…
Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. The intrinsic model dependence makes it necessary to formulate specific…
The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
Since stroke is the main cause of various cerebrovascular diseases, deep learning-based stroke lesion segmentation on magnetic resonance (MR) images has attracted considerable attention. However, the existing methods often neglect the…
A new type of spectroscopy for high-resolution studies of spin waves that relies on resonant scattering of hard x-rays is introduced. The energy transfer in the scattering process is encoded in the precession of the polarization vector of…
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…
The observation of the polarization emerging from a rotating star at different phases opens up the possibility to map the magnetic field in the stellar surface thanks to the well-known Zeeman Doppler Imaging. When the magnetic field is…
This paper addresses the modelling issue of the linearly-polarized solar limb spectrum, which is due to scattering processes and it offers a rich diagnostic potential for exploring solar magnetic fields via the Hanle effect. However, this…
Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…
To interpret observations of astrophysical disks it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, Non-Local…
This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet…
This paper presents a numerical application of a self-consistent theory of partial redistribution in non-LTE conditions, developed in previous papers of the series. The code was described in a previous paper of this series. However, in that…
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as $\mathcal{O}(\frac{N}{P})$, where $N$ is the number of volume…