Related papers: A variational method for quantitative photoacousti…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of…
We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original…
This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where the source is assumed to be driven by a Gaussian random field. The direct problem is shown to be well-posed by…
This paper is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourier transform of a time-dependent source…
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving…
This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In the first one, the…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the…
We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…
Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
This paper is concerned with the stability issue in determining absorption and diffusion coefficients in photoacoustic imaging. Assuming that the medium is layered and the acoustic wave speed is known we derive global H\"{o}lder stability…
We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot…
This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…