Higher Order Numerical Methods for Transient Wave Equations

Book Description
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.

Book Info
Surveys higher-order finite difference methods and develops various mass-lumped finite element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem.


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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.FROM THE REVIEWS: "...The first book to address specifically the use of high-order discretizations in the time domain to solve wave equations ... Cohen's book should be useful, especially to new researchers, and could even be a reference in a course ... I recommend the book for its clear and cogent coverage of the material selected by its author." -PHYSICS TODAY MATHEMATICAL REVIEWS "The author finds in this book the right balance between theoretical and numerical analysis...The book should be very useful to all of the graduate students, scientists, and engineers who want to learn the basics of the numerical analysis of time-dependent wave equations, and to the more advanced researchers who want a thorough and up-to-date presentation on the discretization of first-order hyperbolic systems."


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