A primer on radial basis functions with applications to the geosciences / Bengt Fornberg, University of Colorado, Boulder, Colorado, Natasha Flyer, National Center for Atmospheric Research, Boulder, Colorado.
CBMS-NSF regional conference series in applied mathematics ; 87. [More in this series]
CBMS-NSF regional conference series in applied mathematics ; 87 [More in this series]
Summary note
Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.
Notes
Bibliographic Level Mode of Issuance: Monograph
Bibliographic references
Includes bibliographical references and index.
System details
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Source of description
Title from title screen, viewed 8/27/2015.
Language note
English
Contents
Preface
1. Brief summary of finite difference methods
2. Brief summary of pseudospectral methods
3. Introduction to radial basis functions
4. Global RBFs for solving PDEs
5. RBF-generated FD (RBF-FD) methods
6. Global RBF applications to geo-modeling: spherical domains
7. RBF-FD applications to geo-modeling: spherical domains
8. RBF-FD applications to geo-modeling: limited-area domains
Appendix A. Introduction to RBFs via cubic splines
Appendix B. Spherical harmonics
Appendix C. Some node distribution strategies
Appendix D. Cartesian vector operators on a sphere.
ISBN
1-61197-404-6
Publisher no.
CB87
OCLC
919539534
Doi
10.1137/1.9781611974041
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