Related papers: Approximating moving point sources in hyperbolic p…
This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, $X_\mathrm{s}(t) = vt$ is the location of the…
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the…
In this paper, we address the problem of recovering point sources from two dimensional low-pass measurements, which is known as super-resolution problem. This is the fundamental concern of many applications such as electronic imaging,…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
We consider the sound ranging problem, which is to find the position of the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points, in the infinite-dimensional separable…
In this paper, we consider the 1D wave equation where the spatial domain is a bounded interval. Assuming the initial conditions to be known, we are here interested in identifying an unknown source term, while we take the Neumann derivative…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a…
This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to…
We consider the sound ranging, or source localization, problem - find the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points - in the proper metric spaces (any closed ball…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation…
In this paper, we develop a numerical multiscale method to solve elliptic boundary value problems with heterogeneous diffusion coefficients and with singular source terms. When the diffusion coefficient is heterogeneous, this adds to the…