عنوان

A primer on radial basis functions with applications to the geosciences /

(Number (ISBN

161197402X

(Number (ISBN

9781611974027

Title Proper

A primer on radial basis functions with applications to the geosciences /

General Material Designation

[Book]

First Statement of Responsibility

Bengt Fornberg, University of Colorado, Boulder, Colorado, Natasha Flyer, National Center for Atmospheric Research, Boulder, Colorado.

Place of Publication, Distribution, etc.

Philadelphia :

Name of Publisher, Distributor, etc.

SIAM, Society for Industrial and Applied Mathematics,

Date of Publication, Distribution, etc.

[2015]

Date of Publication, Distribution, etc.

©2015

Specific Material Designation and Extent of Item

x, 221 pages :

Other Physical Details

illustrations ;

Dimensions

25 cm.

Series Title

CBMS-NSF regional conference series in applied mathematics ;

Volume Designation

87

Text of Note

Includes bibliographical references (pages 201-218) and index.

Text of Note

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.

0

Text of 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.

Geology-- Mathematical models.

Radial basis functions.

Geology-- Mathematical models.

Geowissenschaften

Mathematisches Modell

Radial basis functions.

Radiale Basisfunktion

Number

Edition

Class number

Book number

Class number

System Code

Fornberg, Bengt.

Flyer, Natasha.

Date of Transaction

20200823050050.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y