Overview
- This book presents classes of methods appearing that are able to solve a wide range of Helmholtz problems
- Not only theoretical results are given, the algorithms are also presented in such a way that they can be used in practical applications
- This volume provides industrial examples
Part of the book series: Geosystems Mathematics (GSMA)
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Table of contents (9 chapters)
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Front Matter
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Algorithms: New Developments and Analysis
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Front Matter
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Algorithms: Practical Methods and Implementations
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Front Matter
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Implementations and Industrial Applications
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Front Matter
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Keywords
About this book
This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts:
new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications.
The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle.
The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra.
Editors and Affiliations
Bibliographic Information
Book Title: Modern Solvers for Helmholtz Problems
Editors: Domenico Lahaye, Jok Tang, Kees Vuik
Series Title: Geosystems Mathematics
DOI: https://doi.org/10.1007/978-3-319-28832-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2017
Hardcover ISBN: 978-3-319-28831-4Published: 10 March 2017
Softcover ISBN: 978-3-319-80436-1Published: 17 July 2018
eBook ISBN: 978-3-319-28832-1Published: 02 March 2017
Series ISSN: 2510-1544
Series E-ISSN: 2510-1552
Edition Number: 1
Number of Pages: XII, 243
Number of Illustrations: 15 b/w illustrations, 39 illustrations in colour
Topics: Numerical Analysis, Partial Differential Equations, Linear and Multilinear Algebras, Matrix Theory, Difference and Functional Equations