Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile

Mathematics of Computing -- Numerical Analysis.

This proceedings consists of 162 selected papers presented at the 2nd Annual International Conference on Mechanics and Mechanical Engineering (MME2015), which was successfully held in Chengdu, China between December 25-27, 2015.MME2015 is one of the key international conferences in the fields of mechanics, mechanical engineering. It offers a great opportunity to bring together researchers and scholars around the globe to deliver the latest innovative research and the most recent developments in the field of Mechanics and Mechanical Engineering.MME2015 received over 400 submissions from about 600 laboratories, colleges and famous institutes. All the submissions have undergone double blind reviewed to assure the quality, reliability and validity of the results presented. These papers are arranged into 6 main chapters according to their research fields. These are: 1) Applied Mechanics 2) Mechanical Engineering and Manufacturing Technology 3) Material Science and Material Engineering 4) Automation and Control Engineering 5) Electrical Engineering 6) System Modelling and Simulation.This proceedings will be invaluable to academics and professionals interested in Mechanics and Mechanical Engineering.

This volume contains results gained from the EU-funded 6th Framework project ADIGMA (Adaptive Higher-order Variational Methods for Aerodynamic Applications in Industry). The goal of ADIGMA was the development and utilization of innovative adaptive higher-order methods for the compressible flow equations enabling reliable, mesh independent numerical solutions for large-scale aerodynamic applications in aircraft industry. The ADIGMA consortium was comprised of 22 organizations which included the main European aircraft manufacturers, the major European research establishments and several universities, all with well proven expertise in Computational Fluid Dynamics (CFD). The book presents an introduction to the project, exhibits partners’ methods and approaches and provides a critical assessment of the newly developed methods for industrial aerodynamic applications. The best numerical strategies for integration as major building blocks for the next generation of industrial flow solvers are identified.

Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.

Mathematics of Computing -- Numerical Analysis.

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications discusses algorithmic developments in the context of genetic algorithms (GAs) and genetic programming (GP). It applies the algorithms to significant combinatorial optimization problems and describes structure identification using HeuristicLab as a platform for al