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.

Résumé

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.

Contenu

A Unified Approach to Finite and Boundary Element Discretization in Linear Time-Harmonic Acoustics.- A Unified Approach to Finite and Boundary Element Discretization in Linear Time-Harmonic Acoustics.- FEM: Numerical Aspects.- Dispersion, Pollution, and Resolution.- Different Types of Finite Elements.- Multifrequency Analysis using Matrix Padé-via-Lanczos.- Computational Aeroacoustics based on Lighthill's Acoustic Analogy.- FEM: External Problems.- Computational Absorbing Boundaries.- Perfectly Matched Layers.- Infinite Elements.- Efficient Infinite Elements based on Jacobi Polynomials.- FEM: Related Problems.- Fluid-Structure Acoustic Interaction.- Energy Finite Element Method.- BEM: Numerical Aspects.- Discretization Requirements: How many Elements per Wavelength are Necessary?.- Fast Solution Methods.- Multi-domain Boundary Element Method in Acoustics.- Waveguide Boundary Spectral Finite Elements.- BEM: External Problems.- Treating the Phenomenon of Irregular Frequencies.- A Galerkin-type BE-formulation for Acoustic Radiation and Scattering of Structures with Arbitrary Shape.- Acoustical Radiation and Scattering above an Impedance Plane.- Time Domain Boundary Element Method.- BEM: Related Problems.- Coupling a Fast Boundary Element Method with a Finite Element Formulation for Fluid-Structure Interaction.- Inverse Boundary Element Techniques for the Holographic Identification of Vibro-Acoustic Source Parameters.