SFB 438: Mathematical Modelling, Simulation and Verification in Material Related Processes and Intelligent Systems

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The development of new materials and material-depending system components with specific, purpose-conform properties has opened many technological opportunities in recent years. This includes the use of varied materials like shape memory alloys, polymere fluids and materials with specific electric and magnetic properties in areas of application ranging from car industry through microelectronics, robotics and process engineering to human medicine. The aim of the collaborative research centre consists in the development, by interdisciplinary cooperation, of improved models for material-depending processes and systems. Furthermore, these models will be validated by efficient numerical simulations based on experimental data.The mathematical approach in the sub-projects is uniformly characterized by the investigation of strongly coupled non-linear systems of partial and ordinary differential equations. The numerics is mainly concentrated on non-linearities, coupling effects, as well as complicated domains of definition. For this purpose, finite-volume- and finite-element-methods, in connection with grid adaptation, multilevel procedures, domain decomposition, and parallelization will be developed and used. In addition, methods of molecular dynamics (Monte Carlo) and multiple shooting procedures will be persued further.