Spline Functions

This book is a continuation of the author's earlier book Spline Functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the last ten years that make use of splines to approximate functions and data and to solve boundary-value problems. The first half of the book works with bivariate spaces of splines defined on H-triangulations, T-meshes, and curved triangulations. Trivariate tensor-product splines and splines on tetrahedral partitions are also discussed. The second half of the book makes use of these spaces to solve boundary-value problems, with a special emphasis on elliptic PDEs defined on curved domains. The book contains numerous examples and figures to illustrate the methods and their performance. In addition to the included bibliography, a 125-page list of additional references can be downloaded from the SIAM website. All of the algorithms in the book have been coded in MATLAB and are included in a package that can also be downloaded from the website. It can be used to run all of the examples in the book. The package also provides an extensive toolbox of functions that readers can utilize to develop their own spline software. The book is designed for mathematicians, engineers, scientists, and anyone else wanting to make use of spline functions for numerical computation.