Mathematics of Wave Phenomena

Mathematics of Wave Phenomena PDF

Author: Willy Dörfler

Publisher: Birkhäuser

Published: 2020-12-07

Total Pages: 325

ISBN-13: 9783030471736

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Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

Mathematical Modelling of Wave Phenomena

Mathematical Modelling of Wave Phenomena PDF

Author: Börje Nilsson

Publisher: American Institute of Physics

Published: 2006-05-12

Total Pages: 406

ISBN-13:

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This conference series intends to illuminate the relationship between different types of waves. This second conference focused primarily on classical wave modeling of acoustic waves in solids and fluids, electromagnetic waves, as well as elastic wave modeling, and both direct and inverse problems are addressed. Topics included are: (1) Classical linear wave propagation modeling, analysis and computation: general, electromagnetic applications, acoustics of fluids, acoustics of solids; (2) classical nonlinear wave propagation modeling, analysis, and computation; (3) inverse scattering modeling: gneral and electromagnetic imaging, wood imaging, seismic imaging; (4) quantum and statistical mechanics; (5) signal processing and analysis.

Mathematical and Numerical Aspects of Wave Propagation WAVES 2003

Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 PDF

Author: Gary Cohen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 923

ISBN-13: 3642558569

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This volume includes articles on the mathematical modeling and numerical simulation of various wave phenomena. For many years Waves 2003 and its five prior conferences have been an important forum for discussions on wave propagation. The topic is equally important for fundamental sciences, engineering, mathematics and, in particular, for industrial applications. Areas of specific interest are acoustics, electromagnetics, elasticity and related inverse and optimization problems. This book gives an extensive overview of recent developments in a very active field of scientific computing.

Wave Phenomena

Wave Phenomena PDF

Author: Willy Dörfler

Publisher: Springer Nature

Published: 2023-03-30

Total Pages: 368

ISBN-13: 3031057937

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This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

Mathematical Methods for Wave Phenomena

Mathematical Methods for Wave Phenomena PDF

Author: Norman Bleistein

Publisher: Academic Press

Published: 2012-12-02

Total Pages: 360

ISBN-13: 0080916953

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Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.

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