Higher-order numerical methods for transient wave equations
348 pages, parution le 15/07/2001
Résumé
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.
Contents
- Part I Basics Definitions and Properties
- The Basic Equations
- Functional Issues
- Plane Wave Solutions
- Part II Finite Difference Methods
- 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 bu Energy Techniques
- Reflection-Transmission Analysis
- Part III Finite Element Methods
- Mass-Lumping in 1D
- Spectral Elements
- Mass Lumped Mixed Formulations and Edge Elements
- Modeling Unbounded Domains
- Appendix Construction of o Général H(curl)-Conforming Transform
- Bibliography
- Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Gary C Cohen |
| Parution | 15/07/2001 |
| Nb. de pages | 348 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 666g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540415985 |
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