Finite Element Analysis of Acoustic Scattering

Author: Frank Ihlenburg
Publisher: Springer Science & Business Media
ISBN: 0387227008
Format: PDF, Docs
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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
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832531394
Format: PDF, ePub
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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
Publisher: Birkhäuser
ISBN: 3319288326
Format: PDF, ePub, Mobi
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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
Publisher: Springer Science & Business Media
ISBN: 9780387205748
Format: PDF, ePub
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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.

Inverse Acoustic and Electromagnetic Scattering Theory

Author: David Colton
Publisher: Springer Science & Business Media
ISBN: 9783540628385
Format: PDF, ePub
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This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

Computational Acoustics of Noise Propagation in Fluids Finite and Boundary Element Methods

Author: Steffen Marburg
Publisher: Springer Science & Business Media
ISBN: 9783540774488
Format: PDF, ePub
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The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimization) for acoustics. The book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation.

Numerical Analysis of Multiscale Problems

Author: Ivan G. Graham
Publisher: Springer Science & Business Media
ISBN: 3642220614
Format: PDF, ePub, Docs
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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.