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

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Steffen Marburg, Bodo Nolte
Springer Science & Business Media, Feb 27, 2008 - Science - 578 pages
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Among numerical methods applied in acoustics, the Finite Element Method (FEM)  is normally favored for interior problems whereas the Boundary Element Method (BEM) is quite popular for exterior ones.

That is why this valuable reference provides a complete survey of methods for computational acoustics, namely FEM and BEM. It demonstrates that both methods can be effectively used in the complementary cases.

The chapters by well-known authors are evenly balanced: 10 chapters on FEM and 10 on BEM. An initial conceptual chapter describes the derivation of the wave equation and supplies a unified approach to FEM and BEM for the harmonic case. A categorization of the remaining chapters and a personal outlook complete this introduction. In what follows, both FEM and BEM are discussed in the context of very different problems.

Firstly, this comprises numerical issues, e.g. convergence, multi-frequency solutions and highly efficient methods; and secondly, solutions techniques for the particular difficulties that arise with external problems, e.g. discussion of absorbing boundaries for FEM and treatment of the non-uniqueness problem for BEM. Finally, both parts on FEM and on BEM are completed by chapters on related problems, e.g. formulations for fluid-structure interaction. In addition to time-harmonic problems, transient problems are considered in some chapters. Many theoretical and industrial applications are presented.

Overall, this book is a unified review of the state-of-the-art on FEM and BEM for computational acoustics.

 

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Contents

Dispersion Pollution and Resolution
36
Different Types of Finite Elements
57
Multifrequency Analysis using Matrix PadéviaLanczos
89
Computational Aeroacoustics based on Lighthills Acoustic Analogy
115
FEM External Problems
143
Computational Absorbing Boundaries
145
Perfectly Matched Layers
167
Infinite Elements
197
Fast Solution Methods
333
Multidomain Boundary Element Method in Acoustics
367
Waveguide Boundary Spectral Finite Elements
387
BEM External Problems
409
Treating the Phenomenon of Irregular Frequencies
410
A Galerkintype BEformulation for Acoustic Radiation and Scattering of Structures with Arbitrary Shape
435
Acoustical Radiation and Scattering above an Impedance Plane
459
Time Domain Boundary Element Method Sabine Langer1 and Martin Schanz2
495

Efficient Infinite Elements based on Jacobi Polynomials
231
FEM Related Problems
251
FluidStructure Acoustic Interaction
252
Energy Finite Element Method
287
BEM Numerical Aspects
307
Discretization Requirements How many Elements per Wavelength are Necessary?
309
BEM Related Problems
517
Coupling a Fast Boundary Element Method with a Finite Element Formulation for FluidStructure Interaction
519
Inverse Boundary Element Techniques for the Holographic Identification of VibroAcoustic Source Parameters
547
Index
573
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Page 55 - Multiscale Phenomena: Green's Functions, the Dirichlet-to-Neumann Formulation, Subgrid Scale Models, Bubbles and the Origins of Stabilized Methods", Comput.
Page 54 - Dispersion and pollution of the fem solution for the Helmholtz equation in one, two and three dimensions.
Page 56 - The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 181:43-69.
Page 57 - INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France...
Page 53 - Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM Journal on Numerical Analysis 34:2392-2423, (2000) Reprinted in SIAM Review 42:451-484 4.

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