Related papers: Mathematical Modelling and a Numerical Solution fo…
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion…
In this article, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular…
We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian model, averaged over fast angles,…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in…
In this article we present a general method to rigorously prove existence of strong solutions to a large class of autonomous semi-linear PDEs in a Hilbert space $H^{l}\subset H^{s}(\mathbb{R}^{m})$ ($s\geq1$) via computer-assisted proofs.…
The photometric precision, monitoring baselines, and rapid, even sampling rates required by modern satellites designed for detecting the signal of transiting exoplanets are ideally suited to a large number of applications in high-energy…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
Air-bearing platforms for simulating the rotational dynamics of satellites require highly precise ground truth systems. Unfortunately, commercial motion capture systems used for this scope are complex and expensive. This paper shows a novel…
Numerical integration of orbit trajectories for a large number of initial conditions and for long time spans is computationally expensive. Semi-analytical methods were developed to reduce the computational burden. An elegant and widely used…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…
A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a…
Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom-Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for…
Numerical models based on physics represent the state-of-the-art in earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model…
This study aims to establish an analytical model that reproduces the gravitational field around non-spherical bodies with constant density. Due to the non-spherical geometry of such bodies, their gravitational potential is disturbed…
We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field. We discretize the Helmholtz equation using finite…
Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…
We use the corrections to the Newton-Einstein secular precessions of the longitudes of perihelia of some planets (Mercury, Earth, Mars, Jupiter, Saturn) of the Solar System, phenomenologically estimated as solve-for parameters by the…
Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows…