Related papers: Approximating moving point sources in hyperbolic p…
Sub-diffraction-limit resolution, or super-resolution, had been successfully demonstrated by recent theoretical and experimental studies for two-point sources with ideal equal-brightness and strict incoherenceness. Unfortunately, practical…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
We consider the radiation transfer problem in the discrete-ordinate, plane-parallel approach. We introduce two benchmark problems with exact known solutions and show that for strongly non-homogeneous media the homogeneous layers…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
We present novel solutions to the problem of direct localization of multiple narrow-band and arbitrarily correlated sources by partly calibrated arrays, i.e., arrays composed of fully calibrated sub-arrays yet lacking inter-array…
We consider linear and nonlinear hyperbolic SPDEs with mixed derivatives with additive space-time Gaussian white noise of the form $Y_{xt}=F(Y) + \sigma W_{xt}.$ Such equations, which transform to linear and nonlinear wave equations,…
We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…