Effective Computational Methods for Wave Propagation

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Nikolaos A. Kampanis, Vassilios Dougalis, John A. Ekaterinaris
CRC Press, Feb 25, 2008 - Mathematics - 712 pages
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Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology.

Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics.

Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.

 

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Contents

Numerical Simulations of Singular Solutions of the Nonlinear Schrodinger Equations
7
Numerical Solution of the Nonlinear Helmholtz Equation
37
Theory and Numerical Analysis of Boussinesq Systems A Review
63
The Helmholtz Equation and Its Paraxial Approximations in Underwater Acoustics
111
Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide
113
Parabolic Equation Techniques in Underwater Acoustics
135
Numerical Solution of the Parabolic Equation in RangeDependent Waveguides
175
Exact Boundary Conditions for Acoustic PE Modeling Over an N2Linear HalfSpace
209
Finite Element Methods with Discontinuous Displacement
331
Fictitious Domains Methods for Wave Diffraction
359
Space Time Mesh Refinement Methods
385
Numerical Methods for Treating Unbounded Media
425
Waves in Compressible Flows
473
HighOrder Accurate Space Discretization Methods for Computational Fluid Dynamics
475
Governing Equations
485
HighOrder FiniteDifference Schemes
491

Numerical Methods for Elastic Wave Propagation
239
Introduction and Orientation
241
The Mathematical Model for Elastic Wave Propagation
247
Finite Element Methods with Continuous Displacement
267
ENO and WENO Schemes
521
The Discontinuous Galerkin DG Method
593
Index
681
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