Barbara I. Wohlmuth - Böcker

Understanding the interaction between various processes is a pre-requisite for solving problems in natural and engineering sciences. Many phenomena can not be described by concentrating on them in isolation - therefore multifield models and concepts that include various kinds of field problems and processes are needed. This book summarizes the main scientific results of the Collaborative Research Center on Multifield Problems in Continuum Mechanics (Sonderforschungsbereich Mehrfeldprobleme in der Kontinuumsmechanik, SFB 404) funded by the German Research Foundation (DFG) from 1995-2006. The book is divided into three main sections: A: Volume-Coupled Problems, devoted to fields which are coupled inside the processing domain or volume, B: Boundary-Coupled Problems, here physical fields and processes are coupled via domain boundaries, C: Fundamental Methods, search into the mathematical concepts and backgrounds of multifield and multiscale modeling.

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.