​Jurgen Steppeler obtained a PhD in  theoretical particle physics and mathematical Physics at the University of Goettingen, Germany. Then he joined the Research Departement of DWD in Offenbach as a specialist for mathematical methods for atmospheric models. During the 50 years since joining DWD he witnessed weather forecasts changing from a form of art involving some guesswork to reliable forecasts entirely produced by computers. He spent long times at other institutes, for example several visits to China. Other vistits were 8 years at ECMWF (European Center for Medium range Forecasts) 1 year at NCEP (National Center or Environmental Prediction, Washington D.C.) and a Series of more than 20 visits of one month each at FSU and NCAR, Boulder. He is a faculty member of University Bonn (Germany), where he supervised a number of PhD theses on mathematical methods in atmospheric models and gave lectures both on numerical methods and about the  cooperation between Universities and  operational institutes. He was Editor and served as reviewer for many scientific Journals. He was project manager of DWD's model LM, which since then was renamed COSMO and ICON and still is part of the numerical forecasting system of DWD. He founded a company to produce software for the cooperation of individuals and institutes on spherical grids and cut cells. Jinxi Li is an Associate Professor at International Center for Climate and Environment Sciences, Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences. He has 6 years’ experience in developing numerical methods and dynamical framework of atmospheric models.  Jinxi earned his Bachelor of Science degree in Mathematics and Applied Mathematics at Hunan Normal University in 2011. He was awarded his doctoral degree in 2016 from the University of Chinese Academy of Sciences. After graduation, he conducted a five-year postdoctoral research in IAP for the development of adaptive mesh atmospheric models collaborated with AMCG, Imperial College London and DAMTP, University of Cambridge.

• Chapter 1. Simple Finite Difference Schemes.- Chapter 2. Basis Functions and Simple L-Galerkin Schemes in 1-d: Galerkin.- Chapter 3. Basis Functions for Triangular Meshes.- Chapter 4. 2-d Sparse Full and Sparse Grids for Quadrilaterals.- Chapter 5. Hexagonal Grids and Hexagonal Sparse Grids.- Chapter 6. Numerical Tests.- Chapter 7. Hexagonal Options.- Chapter 8. Construction of Platonic and Related Bodies on the Sphere.- Chapter 9. Euclids Lemma and the Construction of Quasi Regular Grids on Bilinear Surfaces.- Chapter 10. Differentiation on Curved Surfaces and Modeling on Spheres, Ellipsoids and the Potato Shaped Earth.- Chapter 11. The Construction of the Hexagonal Sub Grid for a Rhomboidal Grid on the Sphere: Sparse Hexagonal Grids.- Chapter 12. Tests on the Sphere.- Chapter 13. The 3-d Small Earth Test Program.- Chapter 14. Regularization of Rhomboidal and Hexagonal Grids.- Chapter 15. Introduction to the MOW Service Library. Chapter 16. Appendix: Tutorial Programs.