Direct and Inverse Problems in Wave Propagation and Applications

This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences.

Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems.

This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits.

The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.

Auteur

Ivan Graham, University of Bath, UK; Ulrich Langer, University of Linz, Austria; Jens Markus Melenk, Vienna University of Technology, Austria; Mourad Sini, RICAM, Linz, Austria.

Contenu

The contributions present the state of the art in modeling, numerical methods and applications by experts in the field.

Contribution 1 by Johannes Elschner & Guanghui Hu (WIAS Berlin) discusses the state of the art for grating problems.

Contribution 2 by Frederic Nataf (Paris) surveys the field of absorbing boundary conditions.

Contribution 3 by Roland Potthast (DWD & Reading) is concerned with wave propagation problems in weather forecasting.

Contribution 4 by Ronny Ramlau (Linz) discusses direct and inverse problems in adaptive optics.

Contributions 5 by Ralf Hiptmair (ETH Zurich) and 6 by Olaf Steinbach (TU Graz) survey boundary element techniques for scattering problems.

Contribution 7 by Habib Ammari (ENS Paris) focuses on aspects of electromagnetic invisibility.

Contribution 8 by Martin Gander (Geneva) and Oliver Ernst (Freiberg) addresses multigrid techniques for Helmholtz problems.

Contribution 9 by Marcus Grote & Teodora Mitkova (Basel) focuses on local timestepping schemes for wave problems.