This survey article deals mainly with two inverse problems and the relation between them.
The first inverse problem we consider is whether one can determine the electrical …

In this chapter, we are interested in finding coefficients of the second-order hyperbolic
operator:(8.0. 1) a0∂ 2 t u+ Au= f in Q= Ω×(0, T) given the initial data (8.0. 2) u= u0,∂ tu= u1 …

A new construction of an absorbing boundary condition for indefinite Helmholtz problems on
unbounded domains is presented. This construction is based on a near-best uniform rational …

The motivation of this work is an inverse problem for the acoustic wave equation, where an
array of sensors probes an unknown medium with pulses and measures the scattered …

To solve an applied inverse problem, a numerical forward model for the problem's physics is
required. Commonly, the finite element method is employed with discretizations consisting of …

We estimate the wave speed in the acoustic wave equation from boundary measurements
by constructing a reduced-order model (ROM) matching discrete time-domain data. The …

Data-driven reduced order models (ROMs) are combined with the Lippmann–Schwinger
integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a …

We introduce a novel nonlinear imaging method for the acoustic wave equation based on
data-driven model order reduction. The objective is to image the discontinuities of the …

We introduce a novel algorithm for nonlinear processing of data gathered by an active array
of sensors which probes a medium with pulses and measures the resulting waves. The …

This work contributes to the numerical solution of the inverse problem of determining an
isotropic conductivity from boundary measurements, known as electrical impedance …