Head:
Robert Lasarzik
Team Assistant:
Anke Giese
Many technological advancements have been driven by innovations in material science. Liquid crystals have enabled the development of modern displays, while semiconductors remain essential for the continuous growth of computational power. Today, several emerging breakthroughs have the potential to spark further innovations. Anisotropic fluids and polymers play a key role in Lab-on-a- Chip devices and human-machine interfaces, while additive manufacturing techniques facilitate the cost-effective production of complex workpieces with tailored properties. The development of these novel technologies depends on the design and production of advanced materials, a process traditionally reliant on costly experiments and prototyping. Mathematical modeling and simulations offer a powerful alternative, significantly reducing costs while enabling the discovery of optimal material properties and production parameters through mathematical optimization. As production processes become increasingly well-documented, the role of mathematics continues to expand. However, real-world mathematical models are often highly nonlinear and strongly coupled, posing significant challenges for conventional mathematical methods. A recent breakthrough — the energy-variational framework — provides a novel approach to rigorously analyzing such complex models. This framework provides the means to develop numerical schemes, simplifying models while quantifying resulting errors, and designing effective control strategies. The aim of the Weierstrass Group is threefold, we will
Robert Lasarzik
Team Assistant:
Anke Giese
Many technological advancements have been driven by innovations in material science. Liquid crystals have enabled the development of modern displays, while semiconductors remain essential for the continuous growth of computational power. Today, several emerging breakthroughs have the potential to spark further innovations. Anisotropic fluids and polymers play a key role in Lab-on-a- Chip devices and human-machine interfaces, while additive manufacturing techniques facilitate the cost-effective production of complex workpieces with tailored properties. The development of these novel technologies depends on the design and production of advanced materials, a process traditionally reliant on costly experiments and prototyping. Mathematical modeling and simulations offer a powerful alternative, significantly reducing costs while enabling the discovery of optimal material properties and production parameters through mathematical optimization. As production processes become increasingly well-documented, the role of mathematics continues to expand. However, real-world mathematical models are often highly nonlinear and strongly coupled, posing significant challenges for conventional mathematical methods. A recent breakthrough — the energy-variational framework — provides a novel approach to rigorously analyzing such complex models. This framework provides the means to develop numerical schemes, simplifying models while quantifying resulting errors, and designing effective control strategies. The aim of the Weierstrass Group is threefold, we will
- use the energy-variational framework to analyze highly nonlinear coupled partial differential equations;
- consider reduced models and hierarchies, derive quantitative error estimates for these reductions;
- implement numerical simulation and optimization tools leading to optimal process or material parameters and designs.
