Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Mathematics of Computing -- General.

The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?

This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.

This book introduces the mathematical concepts that underpin computer graphics. It is written in an approachable way, without burdening readers with the skills of ow to do'things. The author discusses those aspects of mathematics that relate to the computer synthesis of images, and so gives users a better understanding of the limitations of computer graphics systems. Users of computer graphics who have no formal training and wish to understand the essential foundations of computer graphics systems will find this book very useful, as will mathematicians who want to understand how their subject is used in computer image synthesis. '

This book reports on the German research initiative AeroStruct, a three-year collaborative project between universities and the aircraft industry. It describes the development of an integrated multidisciplinary simulation environment for aircraft analysis and optimization using high-fidelity methods. This system is able to run at a high level of automatism, thus representing a step forward with respect to previous ones. Its special features are: a CAD description that is independent from the disciplines involved, an automated CFD mesh generation and an automated structure model generation including a sizing process. The book also reports on test cases by both industrial partners and DLR demonstrating the advantages of the new environment and its suitability for the industry. These results were also discussed during the AeroStruct closing Symposium, which took place on 13-14 October 2015 at the DLR in Braunschweig, Germany. The book provides expert readers with a timely report on multidisciplinary aircraft design and optimization. Thanks to a good balance between theory and practice, it is expected to address an audience of both academics and professional, and to offer them new ideas for future research and development.