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

近年来，具有特定用途特性的新材料和依赖材料的系统部件的开发打开了许多技术机会。这包括使用各种材料，如形状记忆合金、聚合物流体和具有特殊电磁性能的材料，应用领域从汽车工业到微电子、机器人和过程工程到人类医学。合作研究中心的目标是通过跨学科合作，为依赖材料的过程和系统开发改进的模型。此外，这些模型将通过基于实验数据的有效数值模拟来验证。子项目中的数学方法一致地以研究强耦合的非线性偏微分方程组和常微分方程组为特征。数值计算主要集中在非线性、耦合效应以及复杂的定义域上。为此，将开发和使用与网格适应、多层程序、区域分解和并行化相关的有限体积和有限元方法。此外，还将进一步探索分子动力学方法(蒙特卡罗)和多重射击程序。

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.