Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

"Splines and PDEs: From Approximation Theory to Numerical Linear Algebra" offers a comprehensive exploration of the latest mathematical developments in the numerical treatment of partial differential equations (PDEs) using splines, particularly isogeometric methods. The book covers a wide range of research topics, from approximation theory to structured numerical linear algebra. It includes a standalone introduction to B-splines with a special focus on approximation and hierarchical refinement. Additionally, it provides a broad overview of numerical methods for control problems based on B-splines and B-spline-like wavelets. The detailed description of methods for calculating and analyzing the spectral distribution of discretization matrices, as well as the mathematical and implementation aspects of isogeometric analysis, makes this book a valuable resource for students and researchers.