Generic Programming and Algebraic Multigrid: Building Blocks for Scientific Computing

Two topics are in the focus of this book: the generic construction of versatile data structures for numerical linear algebra, as well as the application of algebraic multigrid methods for stabilized flow problems. The first part demonstrates how generic programming and template techniques of C++ can be used to automatically generate highly efficient matrix classes and algorithms. Benchmarks show that this abstract programming approach offers competitive performance in comparison with traditional libraries. In the second and third part, the application of algebraic multigrid to scalar convection-diffusion and linearized Navier-Stokes equations is investigated. A specially adapted method for Oseen problems is introduced, utilizing the point-based ordering of the underlying finite elements. Numerical experiments and comparisons with Krylov methods demonstrate the potential of algebraic multigrid, also for mixed problems. The book is addressed to people in the area of scientific computing and computational fluid dynamics. Because of its interdisciplinary approach, it might be of interest for those who work at the interface between mathematics and computer science.