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Name: Michael NEUNTEUFEL

Current position: Postdoc (Erwin Schrödinger Fellow)
Host: Joachim SCHÖBERL

Many problems in engineering and physics can be described by mathematical equations that govern how quantities evolve in space and time – how a structure deforms, how stresses propagate, or how curvature enters a model. Turning these equations into reliable computer simulations requires numerical methods that not only work in practice but are also well understood from a mathematical point of view. This is the focus of my research.

One key area is shell models, i.e., thin-walled structures such as roofs, car body parts, or landmark buildings like the Sydney Opera House. Shells are lightweight but challenging: their mechanical behaviour depends strongly on geometry and curvature. This is where the finite element method (FEM) meets discrete differential geometry. In simple terms, we translate geometric concepts (such as curvature) into a discrete language that remains consistent and robust across computational meshes. This matters whenever we want trustworthy simulations and to assess and improve the quality of the numerical results.

A second direction concerns more general material behaviour, including metamaterials. Their properties are often governed more by their carefully designed micro-geometry than by the base material. Capturing such effects requires models and discretisations that can represent additional degrees of freedom and geometric information in a controlled manner.

In the midterm, I am also interested in numerical relativity: How can we discretise Einstein’s field equations so that geometric quantities such as curvature remain “correct” even in computations – for example, in simulations around compact objects like black holes? For me, this is an exciting interface where geometry, physics, and scientific computing come together very directly.

What motivates me is turning abstract ideas into practical tools. Besides theory, I also contribute to software so that new methods can actually be used in simulations. Looking ahead, I would like to continue combining research and teaching at the university and hope to build a long-term academic position.