Legacy display Course

V5E3 Advanced Topics in Scientific Computing

Numerical Methods for thin elastic sheets, shapes and isoperimetric problems

Lecturer: Prof. Dr. Martin Rumpf

The lecture course will cover three closely interlinked subjects. In many applications in engineering, in computer vision and in graphics objects and shapes are modeled as thin elastic sheets. In the first part of the course a range of numerical approaches will be presented to efficiently simulate their mechanical behavior and the consistency and convergence of the methods will be analysed.

Secondly, these shape models will be considered as a foundation to develop a geometry in the infinite dimensional space of shapes with applications in shape interpolation, shape animation and transfer of geometric features.

Thirdly, the description of shapes in images is closely linked to image partitioning leading to minimization problems in the space of functions of bounded variation and generalizes classical isoperimetric problems.

The course is coordinated with the lecture course "V5B3 - Analytical methods for thin elastic sheets and isoperimetric problems" by S. Conti (Wednesday 12-14, Thursday 12-14) intending to show the strong interplay between the analytical and computational approaches. Each of these courses will be self contained and can be followed independently. We believe, however, that there will be a substantial gain following both courses in parallel.

Computer lab

In the computer lab we will implement classical finite elements for plate and shell problems, e.g. the Discrete Kirchhoff triangle.