The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

This book combines theory, applications, and numerical methods, and covers each of these
fields with the same weight. In order to make the book accessible to mathematicians …

In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

An improvement to the classical finite element (FE) method is proposed. It is able to exactly
represent the geometry by means of the usual CAD description of the boundary with non …

Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we
extend the study of Veerapaneni et al.[SK Veerapaneni, D. Gueyffier, G. Biros, D. Zorin, A …

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a
bounded, sound soft obstacle in two and three dimensions, studying dependence on the …

We propose a new robust method for the computation of scattering of high-frequency
acoustic plane waves by smooth convex objects in 2D. We formulate this problem by the …

The inverse problem for time-harmonic acoustic wave scattering to recover a sound-soft
obstacle from a given incident field and the far field pattern of the scattered field is …

We present and analyze an infinite dimensional Bayesian inference formulation, and its
numerical approximation, for the inverse problem of inferring the shape of an obstacle from …

We present a numerical comparison of a regularized Newton-type method and a direct
method for reconstructing the surface impedance function of a three dimensional acoustic …