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

Steffen Marburg (auth.), Steffen Marburg, Bodo Nolte (eds.)9783540774471, 3540774475

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.

Table of contents :
Front Matter….Pages I-XIII
A Unified Approach to Finite and Boundary Element Discretization in Linear Time–Harmonic Acoustics….Pages 1-34
Front Matter….Pages 35-35
Dispersion, Pollution, and Resolution….Pages 37-56
Different Types of Finite Elements….Pages 57-88
Multifrequency Analysis using Matrix Padé–via–Lanczos….Pages 89-114
Computational Aeroacoustics based on Lighthill’s Acoustic Analogy….Pages 115-142
Front Matter….Pages 143-143
Computational Absorbing Boundaries….Pages 145-166
Perfectly Matched Layers….Pages 167-196
Infinite Elements….Pages 197-230
Efficient Infinite Elements based on Jacobi Polynomials….Pages 231-250
Front Matter….Pages 251-251
Fluid–Structure Acoustic Interaction….Pages 253-286
Energy Finite Element Method….Pages 287-306
Front Matter….Pages 307-307
Discretization Requirements: How many Elements per Wavelength are Necessary?….Pages 309-332
Fast Solution Methods….Pages 333-366
Multi–domain Boundary Element Method in Acoustics….Pages 367-386
Waveguide Boundary Spectral Finite Elements….Pages 387-408
Front Matter….Pages 409-409
Treating the Phenomenon of Irregular Frequencies….Pages 411-434
A Galerkin–type BE–formulation for Acoustic Radiation and Scattering of Structures with Arbitrary Shape….Pages 435-458
Acoustical Radiation and Scattering above an Impedance Plane….Pages 459-494
Time Domain Boundary Element Method….Pages 495-516
Front Matter….Pages 517-517
Coupling a Fast Boundary Element Method with a Finite Element Formulation for Fluid–Structure Interaction….Pages 519-546
Front Matter….Pages 517-517
Inverse Boundary Element Techniques for the Holographic Identification of Vibro–Acoustic Source Parameters….Pages 547-572
Back Matter….Pages 573-578