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Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methodsby Steffen Marburg
Synopses & Reviews
The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). In particular, the FEM is often used for interior problems whereas BEM is quite popular for exterior problems. This 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 aspects cover the use of different types of elements, discussing the rule of using a fixed number of elements per wavelength and iterative solution techniques for the arising system of equations. Fast boundary element techniques and multi-domain BEM are discussed in this context too. Exterior problems in the context of finite elements will survey different techniques of treatment such as infinite elements, absorbing boundary conditions and perfectly matched layers. Further, the fields of frequency-range solutions by Lanczos via Pade approximation and modal solutions are covered. In the context of BEM, the so-called irregular frequencies are considered. This is followed by considering sound propagation above an impedance plane, formulation of spectral elements, a method for treatment of thin radiators and radiation modes. Both chapters conclude with sections on fluid-structure interaction, on inverse problems and on energy methods, respectively.
Finally, the book discusses future challenges in the field of numerical methods in acoustics.
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.
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
Part I FEM: Numerical Aspects 1 Dispersion, Pollution, and Resolution. 2 Different Types of Finite Elements. 3 Multifrequency Analysis using Matrix Pad´e-via-Lanczos. 4 Computational Aeroacoustics based on Lighthill's Acoustic Analogy. Part II FEM: External Problems 5 Computational Absorbing Boundaries. 6 PerfectlyMatched Layers. 7 Infinite Elements. 8 Efficient Infinite Elements based on Jacobi Polynomials. Part III FEM: Related Problems 9 Fluid-Structure Acoustic Interaction. 10 Energy Finite Element Method. Part IV BEM: Numerical Aspects 11 Discretization Requirements. 12 Fast Solution Methods. 13 Multi-domain Boundary Element Method in Acoustics. 14 Waveguide Boundary Spectral Finite Elements. Part V BEM: External Problems 15 Treating the Phenomenon of Irregular Frequencies. 16 A Galerkin-type BE-formulation. 17 Acoustical Radiation and Scattering above an Impedance Plane. 18 Time Domain BEM. Part VI BEM: Related Problems 19 Coupling a Fast BEM with a FE-Formulation for Fluid-Structure Interaction. 20 Inverse BE-Techniques for the Holographic Identification of Vibro-Acoustic Source Parameters
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