SPP 1095:  Analysis, Modeling and Simulation of Multiscale Problems

• Subject Area: Mathematics
• Term: from 2000 to 2006
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5470341

This priority programme is dedicated to fundamental questions in themathematical modeling and analysis of problems in physics and engineering, which are characterized by the interaction of effects on different temporal or spatial scales. It is the aim to deepen the understanding of the interplay of different scales, since it is not only of principal theoretical interest but also an important prerequisite for the efficient simulation of large systems. It will be studied which information on the small scales is needed to describe the macroscopic quantities correctly.On the basis of specific applications new mathematical concepts (e.g. like Young or microlocal defect measures) are to be developed. They will be used to derive effective macroscopic models which avoid the explicit resolution of the microstructure. This allows us to derive stable and efficient algorithms for the calculation of suitable macroscopic quantities. The following topics are of major interest:(1) weak-convergence methods, (2) analysis of pattern-forming systems, (3) numerical algorithms and simulation and (4) applications (e.g. microstructures elastic materials, micromagnetism, molecule dynamics, quantum mechanics).

• DFG Programme: Priority Programmes

Projects

• Adiabatic limit for particle- field interaction (Applicant Spohn, Herbert )
• Analysis and numerical treatment of 3-scale interaction for generic energy level crossings in quantum classical molecular dynamics (Applicant Lasser, Caroline )
• Analysis, modeling and simulation of multi-scale, multi-phase solidification in alloy systems (Applicant Nestler, Britta )
• Analysis, Modellbildung und Simulation skalenübergreifender, mehrphasiger Erstarrung in Legierungssystemen (Applicant Garcke, Harald )
• Approximation von Vielteilchen-Wellenfunktionen auf dünnen Gittern (Applicant Kolb, Dietmar )
• Approximation von Vielteilchen-Wellenfunktionen auf dünnen Gittern (Applicant Hackbusch, Wolfgang )
• Composed finite elements for approximating partial differential equations with jumping coefficients (Applicant Hackbusch, Wolfgang )
• Ein Zweiskalenmodell für fest-flüssig Phasenübergänge mit dendritischer Mikrostruktur und Konvektion (Applicant Eck, Christof )
• Elektronische Zustände in Halbleiter-Nanostrukturen und Upscaling auf semiklassische Modelle (Applicant Fuhrmann, Jürgen )
• Essentielle Freiheitsgrade und makroskopische Dynamik molekularer Systeme (Applicant Schütte, Christof )
• Homogenization of liquid phase epitaxy (Applicant Emmerich, Heike )
• Homogenization of liquid phase epitaxy (Applicant Eck, Christof )
• Homogenization of many particle systems (Applicant Niethammer, Barbara )
• Koordinatorantrag im Schwerpunktprogramm "Analysis, Modellbildung und Simulation von Mehrskalenproblemen" (Applicant Mielke, Alexander )
• Makroskopische Dynamik in diskreten Gittern (Applicant Mielke, Alexander )
• Mehrskalensimulation von mechanischer Dispersion in komplexen Mikrostrukturen (Applicant Hilfer, Rudolf )
• Mehrskalensimulation von mechanischer Dispersion in komplexen Mikrostrukturen (Applicant Knabner, Peter )
• Mikro-Makro-Übergänge mittels Modulationstheorie (Applicant Sprekels, Jürgen )
• Multiple scales in phase separating systems with elastic misfit (Applicant Garcke, Harald )
• Multiple scales in phase separating systems with elastic misfit (Applicant Rumpf, Martin )
• Multiple scales in phase separating systems with elastic misfit (Applicant Niethammer, Barbara )
• Multiscale folding patterns in thin elastic sheets (Applicant Conti, Sergio )
• Numerik und Asymptotik mikroskopischer und makroskopischer Gleichungen für Quantensysteme (Applicant Jüngel, Ansgar )
• Numerik und Asymptotik mikroskopischer und makroskopischer Gleichungen für Quantensysteme (Applicant Arnold, Anton )
• Numerische Relaxierung von nichtkonvexen Funktionalen der Festkörpermechanik (Applicant Hackl, Klaus )
• Numerische Relaxierung von nichtkonvexen Funktionalen der Festkörpermechanik (Applicant Carstensen, Carsten )
• Numerische Simulation intrazellulärer Kalzium-Dynamik in lebenden Zellen (Applicant Falcke, Martin )
• Numerische Simulation intrazellulärer Kalzium-Dynamik in lebenden Zellen (Applicant Warnecke, Gerald )
• Numerische Verfahren für Probleme mit mehrfachen Zeitskalen (Applicant Lubich, Christian )
• Phasenübergänge in Kristallen (Applicant Blesgen, Thomas )
• Quantitative Homogenization and Averaging (Applicant Fiedler, Bernold )
• Radiative friction for charges interacting with the radiation field (Applicant Kunze, Markus )
• Resolving Multiscale Structures via Decoupling Techniques (Applicant Dellnitz, Michael )
• Singuläre Limiten diskreter Modelle (Applicant Blesgen, Thomas )
• Skalenlimiten und Modellierung von Strömung und Transport in verzweigten Netzen (Applicant Jäger, Willi )
• Soft Ferromagnetic Films (Applicant Müller, Stefan )
• Structural Optimization of Biomorphic Cellular Silicon Carbide Ceramics with Microstructures by Homogenization Modeling (Applicant Hoppe, Ronald H.W. )
• Structural optimization of biomorphic cellular silicon carbide ceramics with microstructures by homogenization modeling (Applicant Hoppe, Ronald H.W. )
• Thermal decay of nanostructures and Ostwald ripening of homoepitaxial monolayers (Applicant Voigt, Axel )
• Thermodynamics of Phase Changes - Martensitic Transformations, Molecular Analysis, Phase Diagrams (Applicant Müller, Ingo )

• Spokesperson: Professor Dr. Alexander Mielke