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.
Finite Element Analysis of Acoustic Scattering
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Inside This Book
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First Sentence:
Acoustic waves (sound) are small oscillations of pressure P(x, t) in a compressible ideal fluid (acoustic medium). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
analytic shape functions, backscattered pressure, mock shell, elastic spherical shell, radiating solutions, effectivity index, pollution error, discrete wave number, effectivity indices, bubble modes, shifted solution, infinite elements, posteriori error estimation, pollution term, sup condition, high wave numbers, sesquilinear form, static condensation, trial space, finite element solution, coupled problem, acoustic medium, absorbing boundary conditions, exterior problems, edge modes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographical Remarks, Cauchy Schwarz, Convergence of Galerkin, Naval Research Laboratory, The Influence of Damped Resonance New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Acoustic waves (sound) are small oscillations of pressure P(x, t) in a compressible ideal fluid (acoustic medium). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
analytic shape functions, backscattered pressure, mock shell, elastic spherical shell, radiating solutions, effectivity index, pollution error, discrete wave number, effectivity indices, bubble modes, shifted solution, infinite elements, posteriori error estimation, pollution term, sup condition, high wave numbers, sesquilinear form, static condensation, trial space, finite element solution, coupled problem, acoustic medium, absorbing boundary conditions, exterior problems, edge modes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bibliographical Remarks, Cauchy Schwarz, Convergence of Galerkin, Naval Research Laboratory, The Influence of Damped Resonance New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
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24
books
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- Partial Differential Equations: Analytical Solution Techniques (Texts in Applied Mathematics) by J. Kevorkian in Front Matter, and Back Matter
- Periodic Motions (Applied Mathematical Sciences) by Miklos Farkas in Back Matter
- Lectures on Viscoelasticity Theory (Applied Mathematical Sciences) by A.C. Pipkin in Front Matter
- Averaging Methods in Nonlinear Dynamical Systems (Applied Mathematical Sciences) by Jan A. Sanders in Front Matter
- Wave Physics: Oscillations - Solitons - Chaos (Advanced Texts in Physics) by Stephen Nettel in Back Matter
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- Topics in Computational Wave Propagation and Inverse Problems by Mark Ainsworth on page 197
- Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Encyclopedia of Mathematics and its Applications) by P. A. Martin in Back Matter
- Front Tracking for Hyperbolic Conservation Laws by Helge Holden in Back Matter
- Dynamics in Infinite Dimensions by Jack K. Hale in Back Matter
- Random Perturbation Methods by Anatoli V. Skorokhod on page
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