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.

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 application to geo-modeling: limited-area domains; 7. RBF-FD applications to geo-modeling: spherical domains; 8. RBF-FD application to geo-modeling: limited-area domains; A. Introduction to RBFs via cubic splines; B. Spherical harmonics; C. Some node distribution strategies; D. Cartesian vector operators on a sphere; Bibliography; Index.