Related papers: Numerical resolution by the quasi-reversibility me…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
We study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We…
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…
This paper presents a modified quasi-reversibility method for computing the exponentially unstable solution of a nonlocal terminal-boundary value parabolic problem with noisy data. Based on data measurements, we perturb the problem by the…
We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
This work is on the numerical approximation of incoming solutions to Maxwell's equations with dissipative boundary conditions whose energy decays exponentially with time. Such solutions are called asymptotically disappearing (ADS) and they…
A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…
We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the…
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when…