Effective Computational Methods for Wave Propagation: 1st Edition (Hardback) book cover

Effective Computational Methods for Wave Propagation

1st Edition

Edited by Nikolaos A. Kampanis, Vassilios Dougalis, John A. Ekaterinaris

Chapman and Hall/CRC

712 pages | 193 B/W Illus.

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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.

Table of Contents


Nonlinear Dispersive Waves

Numerical Simulations of Singular Solutions of Nonlinear Schrödinger Equations

Xiao-Ping Wang

Numerical Solution of the Nonlinear Helmholtz Equation

G. Fibich and S. Tsynkov

Theory and Numerical Analysis of Boussinesq Systems: A Review

V.A. Dougalis and D.E. Mitsotakis

The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics

Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide

D.A. Mitsoudis, N.A. Kampanis, and V.A. Dougalis

Parabolic Equation Techniques in Underwater Acoustics

D.J. Thomson and G.H. Brooke

Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides

V.A. Dougalis, N.A. Kampanis, F. Sturm, and G.E. Zouraris

Exact Boundary Conditions for Acoustic PE Modeling over an N2-Linear Half-Space

T.W. Dawson, G.H. Brooke, and D.J. Thomson

Numerical Methods for Elastic Wave Propagation

Introduction and Orientation

P. Joly

The Mathematical Model for Elastic Wave Propagation

P. Joly

Finite Element Methods with Continuous Displacement

P. Joly

Finite Element Methods with Discontinuous Displacement

P. Joly and C. Tsogka

Fictitious Domains Methods for Wave Diffraction

P. Joly and C. Tsogka

Space–Time Mesh Refinement Methods

G. Derveaux, P. Joly, and J. Rodríguez

Numerical Methods for Treating Unbounded Media

P. Joly and C. Tsogka

Waves in Compressible Flows

High-Order Accurate Space Discretization Methods for Computational Fluid Dynamics

J.A. Ekaterinaris

Governing Equations

J.A. Ekaterinaris

High-Order Finite-Difference Schemes

J.A. Ekaterinaris

ENO and WENO Schemes

J.A. Ekaterinaris

The Discontinuous Galerkin (DG) Method

J.A. Ekaterinaris


About the Editor

Nikolaos A. Kampanis, Vassilios A. Dougalis, John A. Ekaterinaris

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Number Systems
SCIENCE / Mathematical Physics