A Primer on Radial Basis Functions with Applications to the Geosciences

Bengt Fornberg received his PhD from Uppsala University in Sweden. Following positions at the European Organization for Nuclear Research (CERN), the California Institute of Technology, and Exxon Corporate Research, he has been on the faculty of Applied Mathematics at the University of Colorado Boulder since 1995. His research focus is on numerical methods for solving PDEs and computational methodologies for analytic functions. Natasha Flyer received her PhD from the University of Michigan, Ann Arbor. She is a staff scientist at the National Center for Atmospheric Research in Boulder, Colorado. Her research interests include development of computational methods for solar physics and geosciences and hybrid analytical-numerical methods for the solution of PDEs with singularities.

Chapter 1: Brief Summary of Finite Difference Methods Chapter 2: Brief Summary of Pseudospectral Methods Chapter 3: Introduction to Radial Basis Functions Chapter 4: Global RBFs for Solving PDEs Chapter 5: RBF-Generated FD (RBF-FD) Methods Chapter 6: Global RBF Applications to Geo-Modeling: Spherical Domains Chapter 7: RBF-FD Applications to Geo-Modeling: Spherical Domains Chapter 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