Related papers: Closed Form Fractional Integration and Differentia…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…

In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\mathbb{R}^d$. Our method…

Spectral integration was deployed by Orszag and co-workers (1977, 1980, 1981) to obtain stable and efficient solvers for the incompressible Navier-Stokes equation in rectangular geometries. Two methods in current use for channel flow and…

Consider an input-output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero…

We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…

This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…

Extreme adaptive optics systems are now in operation across the globe. These systems, capable of high order wavefront correction, deliver Strehl ratios of 90% in the near-infrared. Originally intended for the direct imaging of exoplanets,…

We propose a novel approach to approximate numerically shock waves. The method combines the unstructured shock-fitting approach developed in the last decade by some of the authors, with ideas coming from embedded boundary techniques. The…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

A theoretical framework is developed to link the density profiles in the Scrape Off Layer (SOL) with the fluctuations (filaments) that generate them. The framework is based on the dynamics of independent filaments and their statistical…

We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger…

We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…

In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal…

This work presents the implementation, numerical examples and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape…

This paper proposes the design of Fractional Order (FO) Butterworth filter in complex w-plane (w=sq; q being any real number) considering the presence of under-damped, hyper-damped, ultra-damped poles. This is the first attempt to design…

Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently…

Computational spectrometers are pivotal in enabling low-cost, in-situ and rapid spectral analysis, with potential applications in chemistry, biology, and environmental science. However, filter-based spectral encoding approaches typically…

A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their…

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…