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This thesis by Lydie Mpinganzima investigates the Cauchy problem for the Helmholtz equation, which is an ill-posed problem often encountered in technical and scientific fields such as medical and geophysical imaging, astrophysics, and electromagnetic scattering. The author develops and studies alternating iterative algorithms based on the methods suggested by V.A. Kozlov and V. Maz’ya to solve this problem. The thesis includes modifications to these algorithms to ensure convergence for all values of the wave number k² and presents numerical experiments that confirm their efficacy. This work is intended for mathematicians and researchers dealing with partial differential equations and inverse problems.

Helmholtz equation. --- Inverse problems (Differential equations)

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Helmholtz equation --- Waves --- Numerical solutions. --- Diffraction --- Mathematical models.

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This book gives a detailed overview of the theory of electromagnetic wave scattering on single, homogeneous, but nonspherical particles. A related Green’s function formalism is systematically developed which provides a powerful mathematical basis not only for the development of numerical approaches but also to discuss those general aspects like symmetry, unitarity, and the validity of Rayleigh’s hypothesis. Example simulations are performed in order to demonstrate the usefulness of the developed formalism as well as to introduce the simulation software which is provided on a CD-ROM with the book.

Electromagnetic waves --- Particles --- Green's functions --- Helmholtz equation --- Wave equation --- Separation of variables --- Electricity & Magnetism --- Light & Optics --- Physics --- Physical Sciences & Mathematics --- Mathematical models --- Scattering --- Optical properties --- Numerical solutions --- Electromagnetic theory. --- Scattering. --- Light, Electromagnetic theory of --- Physics. --- Optics. --- Electrodynamics. --- Engineering. --- Optics and Electrodynamics. --- Engineering, general. --- Electric fields --- Magnetic fields --- Scattering (Physics) --- Classical Electrodynamics. --- Construction --- Industrial arts --- Technology --- Dynamics --- Light

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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.

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This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.

Engineering. --- Engineering Acoustics. --- Acoustics. --- Vibration, Dynamical Systems, Control. --- Mathematical Modeling and Industrial Mathematics. --- Vibration. --- Acoustics in engineering. --- Ingénierie --- Acoustique --- Vibration --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Sound-waves. --- Sound --- Radiation sources. --- Least squares. --- Helmholtz equation --- Transmission. --- Numerical solutions. --- Method of least squares --- Squares, Least --- Sources of radiation --- Transmission of sound --- Mathematical models. --- Dynamical systems. --- Dynamics. --- Acoustical engineering. --- Numerical analysis --- Curve fitting --- Geodesy --- Mathematical statistics --- Mathematics --- Probabilities --- Triangulation --- Quantum optics --- Radiation --- Architectural acoustics --- Sound-waves --- Soundproofing --- Waves --- Cycles --- Mechanics --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Engineering --- Models, Mathematical --- Simulation methods --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Industrial applications