finite element analysis of acoustic scattering applied mathematical sciences

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Finite Element Analysis Of Acoustic Scattering

Author : Frank Ihlenburg
ISBN : 9780387227009
Genre : Mathematics
File Size : 53. 29 MB
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A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.

Numerical Simulations In Room Acoustics Using Direct Coupling Techniques And Finite Elements

Author : Martina Pospiech
ISBN : 9783832531393
Genre :
File Size : 45. 86 MB
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This thesis presents a coupling approach for time-harmonic problems in linear room acoustics. Therein the closed acoustic system is subdivided into air, sound source and different boundary components. The sound field of each air component is approximated with the help of modal basis functions and continuous transitions between single components are enabled by enforcing coupling conditions. Coupling to realistic boundary conditions is realized by wavenumber- and frequency-dependent impedance functions for plate-like sound absorbers. Afterwards the solution is computed by minimizing the energy based on Hamilton's Principle. For computing the basis functions and the energies of the components the Spectral Finite Element Method and the adapted Patch Recovery Method are applied. Finally numerical benchmark-simulations show the applications of this coupling approach.

Modern Solvers For Helmholtz Problems

Author : Domenico Lahaye
ISBN : 9783319288321
Genre : Mathematics
File Size : 20. 31 MB
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This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra.

Theory And Practice Of Finite Elements

Author : Alexandre Ern
ISBN : 0387205748
Genre : Mathematics
File Size : 82. 18 MB
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This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

Finite Element Methods For Maxwell S Equations

Author : Peter Monk
ISBN : 0198508883
Genre : Mathematics
File Size : 52. 27 MB
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The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.

Linear Integral Equations

Author : Rainer Kress
ISBN : 9781461495932
Genre : Mathematics
File Size : 69. 11 MB
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This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)

Advanced Techniques In Applied Mathematics

Author : Shaun Bullett
ISBN : 9781786340245
Genre : Mathematics
File Size : 45. 76 MB
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This book is a guide to advanced techniques used widely in applied mathematical sciences research. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in techniques such as practical analytical methods, finite elements and symmetry methods for differential equations. Advanced Techniques in Applied Mathematics is the first volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas. Contents:Practical Analytical Methods for Partial Differential Equations (Helen J Wilson)Resonances in Wave Scattering (Dmitry V Savin)Modelling — What is it Good For? (Oliver S Kerr)Finite Elements (Matthias Maischak)Introduction to Random Matrix Theory (Igor E Smolyarenko)Symmetry Methods for Differential Equations (Peter A Clarkson) Readership: Researchers, graduate or PhD mathematical-science students who require a reference book that covers advanced techniques used in applied mathematics research.

Biomedical Applications Of Vibration And Acoustics For Imaging And Characterisations

Author : Mostafa Fatemi
ISBN : STANFORD:36105130544310
Genre : Medical
File Size : 63. 87 MB
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The primary objective of this book is to compile the research topics on biomedical imaging and tissue characterisation techniques that utilise vibration and acoustics.

Acoustic And Electromagnetic Equations

Author : Jean-Claude Nedelec
ISBN : 9781475743937
Genre : Mathematics
File Size : 76. 9 MB
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Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modeling of these waves has undergone considerable growth in recent years, and this timely book, written by a leading international researcher, presents the research in a careful and complete way.

Philosophical Transactions

Author :
ISBN : UCSD:31822033900614
Genre : Physical sciences
File Size : 22. 56 MB
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