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The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical  analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Mathematical models. --- Multiscale modeling. --- Multiscale modeling --- Numerical analysis --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematics - General --- Applied Mathematics --- Models, Mathematical --- Multi-scale modeling --- Multiscale models --- Mathematics. --- Computer mathematics. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Appl.Mathematics/Computational Methods of Engineering. --- Numerical and Computational Physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Simulation methods --- Mathematical models --- Multivariate analysis --- Computer science --- Computer science. --- Mathematical and Computational Engineering. --- Numerical and Computational Physics, Simulation. --- Informatics --- Numerical analysis.

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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.

Radio wave propagation. --- Radio waves --- Diffraction --- Propagation of radio waves --- Wave-motion, Theory of --- Diffraction. --- Scattering. --- Propagation --- 537.8 --- 537.8 Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- Cloaking. --- Finite Element Method. --- Helmholtz Equation. --- Inverse Problem. --- Partial Differential Equation. --- Wave Propagation.