Higher-Order Numerical Methods for Transient Wave Equations

2002
ISBN: 978-3-540-41598-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 349 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 791 g

Reihe: Scientific Computation

"To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003

Zielgruppe

Research

Autoren/Hrsg.

Cohen, Gary

Fachgebiete

• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

I. Basic Definitions and Properties.- 1. The Basic Equations.- 2. Functional Issues.- 3. Plane Wave Solutions.- II. Finite Difference Methods.- 4. Construction of the Schemes in Homogeneous Media.- 5. The Dispersion Relation.- 6. Stability of the Schemes.- 7. Numerical Dispersion and Anisotropy.- 8. Construction of the Schemes in Heterogeneous Media.- 9. Stability by Energy Techniques.- 10. Reflection-Transmission Analysis.- III. Finite Element Methods.- 11. Mass-Lumping in 1D.- 12. Spectral Elements.- 13. Mass-Lumped Mixed Formulations and Edge Elements.- 14. Modeling Unbounded Domains.- A.1.1 Notation.- A.2.1 Notation.