Related papers: A spectral method algorithm for numerical simulati…
Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…
A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
The detection of gravitational waves by the LIGO-Virgo-KAGRA collaboration has ushered in a new era of observational astronomy, emphasizing the need for rapid and detailed parameter estimation and population-level analyses. Traditional…
We present a machine learning-based approach for characterising the environment that affects the dynamics of an open quantum system. We focus on the case of an exactly solvable spin-boson model, where the system-environment interaction,…
In this paper, an oscillation-free spectral volume (OFSV) method is proposed and studied for the hyperbolic conservation laws. The numerical scheme is designed by introducing a damping term in the standard spectral volume method for the…
The route to reliable quantum nanoelectronic devices hinges on precise control of the electrostatic environment. For this reason, accurate methods for electrostatic simulations are essential in the design process. The most widespread…
In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in…
Cosmological random fields are often analysed in spherical Fourier-Bessel basis. Compared to the Cartesian Fourier basis this has an advantage of properly taking into account some of the relevant physical processes (redshift-space…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
We revisit the quasinormal mode (QNM) problem in Schwarzschild--de Sitter spacetimes providing a unified infrastructure tailored for studying limiting configurations. Geometrically, we employ the hyperboloidal framework to explicitly…
In previous works, we suggested considering a (3+1)D quantum gravitational field as an evolution of a (2+1)D renormalized quantum gravitational field along the direction of the gravitational force. The starting point of the suggestion is a…
We review and further develop the recently introduced numerical approach for scattering calculations based on a so called pseudo-time Schroedinger equation, which is in turn a modification of the damped Chebyshev polynomial expansion…
Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical…
We present a numerical scheme for simulating the 2D quantum dynamics of a two-level particle gas with internal degrees of freedom such as spin, pseudo-spin, or a two-band electronic structure. We adopt the Wigner formulation of quantum…
In this work, a recently developed novel solution of the famous "Sommerfeld Radiation Problem" is revisited. The solution is based on an analysis performed entirely in the spectral domain, through which a compact asymptotic formula…
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply…
Spectral embedding uses eigenfunctions of the discrete Laplacian on a weighted graph to obtain coordinates for an embedding of an abstract data set into Euclidean space. We propose a new pre-processing step of first using the eigenfunctions…