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Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.
Front Matter
Front Matter
The Basic Equations
Functional Issues
Plane Wave Solutions
Front Matter
Construction of the Schemes in Homogeneous Media
The Dispersion Relation
Stability of the Schemes
Numerical Dispersion and Anisotropy
Construction of the Schemes in Heterogeneous Media
Stability by Energy Techniques
Reflection-Transmission Analysis
Front Matter
Mass-Lumping in 1D
Spectral Elements
Mass-Lumped Mixed Formulations and Edge Elements
Modeling Unbounded Domains
Back Matter