The simulation of complex engineering problems often involves an interaction or coupling of individual phenomena, which are traditionally related by themselves to separate fields of applied mechanics. Typical examples of these so- called multifield problems are the thermo-mechanical analysis of solids with coupling between mechanical stress analysis and thermal heat transfer processes, the simulation of coupled deformation and fluid transport mechanisms in porous media, the prediction of mass transport and phase transition phenomena of mixtures, the analysis of sedimentation proces- ses based on an interaction of particle dynamics and viscous flow, the simulation of multibody systems and fluid-structure interactions based on solid-to-solid and solid-to-fluid contact mechanisms.

The so-called boundary element methods BEM, i.e. finite element approxima tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re sults and decisive new developments in theory and algorithms. The program was started due to encouragement by E. Stein, when most of the later par ticipants met in Stuttgart at a Boundary Element Conference 1987. Then W. Hackbusch, G. Kuhn, S. Wagner and W. Wendland were entrusted with writing the proposal which was 1988 presented at the German Research Foun dation and started in 1989 with 14 projects at 11 different universities. After German unification, the program was heavily extended by six more projects, four of which located in Eastern Germany. When we started, we were longing for the following goals: 1. Mathematicians and engineers should do joint research. 2. Methods and computational algorithms should be streamlined with re spect to the new computer architectures of vector and parallel computers. 3. The asymptotic error analysis of boundary element methods should be further developed. 4. Non-linear material laws should be taken care of by boundary element methods for crack-mechanics. 5. The coupling of finite boundary elements should be improved."

This book on the state of the art in "Multifield Problems" consists of selected articles based on a conference on this topic at the University of Stuttgart in 1999. The first two articles are contributions to the general modelling of multifield problems. S.S. Antman presents the important role of viscoelastic dissipation in the mathematical modelling of bifurcation analysis of nonlinear elasticity for large deformations. G.A. Maugin presents the basic theoretical foundations for the combination of three scales - the microscopic lattice of crystals, the mesoscopic thermomechanical model and the macroscopic con tinuum mechanics model for describing the propagation of phase transition fronts in terms of the Landau-Ginzburg theory and the modelling of nonlinear waves. The other contributions are associated with five main areas of multifield modelling such as two and multiphase flows, the mechanics of materials in terms of multiscaling, the interaction of solids and fluids, efficient solution methods of the discrete equations including adaptivity, and the modelling of contact and fracture."