A survey on inverse problems for applied sciences
type: Item
instance of: scholarly article
title: A survey on inverse problems for applied sciences
zbMATH Open document ID: 1299.35321
author: Fatih Yaman
author: V. G. Yakhno
author: Roland Potthast
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 86A20
zbMATH DE Number: 6372755
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6372755