Effective Computational Methods for Wave Propagation

Preface. Nonlinear Dispersive Waves: Numerical Simulations of Singular Solutions of Nonlinear Schrödinger Equations. Numerical Solution of the Nonlinear Helmholtz Equation. Theory and Numerical Analysis of Boussinesq Systems: A Review. The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics: Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide. Parabolic Equation Techniques in Underwater Acoustics. Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides. Exact Boundary Conditions for Acoustic PE Modeling over an N2-Linear Half-Space. Numerical Methods for Elastic Wave Propagation. Introduction and Orientation. The Mathematical Model for Elastic Wave Propagation. Finite Element Methods with Continuous Displacement. Finite Element Methods with Discontinuous Displacement. Fictitious Domains Methods for Wave Diffraction. Space Time Mesh Refinement Methods. Numerical Methods for Treating Unbounded Media. Waves in Compressible Flows. High-Order Accurate Space Discretization Methods for Computational Fluid Dynamics. Governing Equations. High-Order Finite-Difference Schemes. ENO and WENO Schemes. The Discontinuous Galerkin (DG) Method. Index.