Finite Element Analysis of Acoustic Scattering

Author: Frank Ihlenburg
Publisher: Springer Science & Business Media
ISBN: 0387227008
Format: PDF, ePub, Mobi
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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, Mobi
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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.

Theory and Practice of Finite Elements

Author: Alexandre Ern
Publisher: Springer Science & Business Media
ISBN: 9780387205748
Format: PDF, Docs
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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.

Progress in Computational Physics PiCP

Author: Matthias Ehrhardt
Publisher: Bentham Science Publishers
ISBN: 1608051501
Format: PDF
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Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. the series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. Periodic structure problems arise quite often in many modern application areas like semiconductor nanostructures (e.g. quantum dots and nanocrystals), semiconductor superlattices, photonic crystals structures, meta materials or Bragg gratings of surface plasmon polariton waveguides. This first volume treats both mathematical analysis of periodic structure problems and state-of-the art numerical techniques, such as frequency domain methods, beam propagation methods and eigenmode expansion methods. Several chapters are devoted to concrete applications of periodic media simulation. the book is a useful resource for individuals interested in complex wave mechanics of unique physical structures.

Finite Element Methods for Maxwell s Equations

Author: Peter Monk
Publisher: Oxford University Press
ISBN: 9780198508885
Format: PDF, ePub, Mobi
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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.

Finite Element and Boundary Methods in Structural Acoustics and Vibration

Author: Noureddine Atalla
Publisher: CRC Press
ISBN: 1466592885
Format: PDF, ePub
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Effectively Construct Integral Formulations Suitable for Numerical Implementation Finite Element and Boundary Methods in Structural Acoustics and Vibration provides a unique and in-depth presentation of the finite element method (FEM) and the boundary element method (BEM) in structural acoustics and vibrations. It illustrates the principles using a logical and progressive methodology which leads to a thorough understanding of their physical and mathematical principles and their implementation to solve a wide range of problems in structural acoustics and vibration. Addresses Typical Acoustics, Electrodynamics, and Poroelasticity Problems It is written for final-year undergraduate and graduate students, and also for engineers and scientists in research and practice who want to understand the principles and use of the FEM and the BEM in structural acoustics and vibrations. It is also useful for researchers and software engineers developing FEM/BEM tools in structural acoustics and vibration. This text: Reviews current computational methods in acoustics and vibrations with an emphasis on their frequency domains of applications, limitations, and advantages Presents the basic equations governing linear acoustics, vibrations, and poroelasticity Introduces the fundamental concepts of the FEM and the BEM in acoustics Covers direct, indirect, and variational formulations in depth and their implementation and use are illustrated using various acoustic radiation and scattering problems Addresses the exterior coupled structural–acoustics problem and presents several practical examples to demonstrate the use of coupled FEM/BEM tools, and more Finite Element and Boundary Methods in Structural Acoustics and Vibration utilizes authors with extensive experience in developing FEM- and BEM-based formulations and codes and can assist you in effectively solving structural acoustics and vibration problems. The content and methodology have been thoroughly class tested with graduate students at University of Sherbrooke for over ten years.

Advanced Techniques in Applied Mathematics

Author: Shaun Bullett
Publisher: World Scientific
ISBN: 1786340240
Format: PDF, Kindle
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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.