Periodic Reporting for period 1 - GLnQuadRemeshing (Re-meshing of a given triangle mesh surface to a quad mesh using physically motivated methods based on the Ginzburg--Landau potential and solved efficiently solved via numerical splitting scheme)
Reporting period: 2018-10-01 to 2020-09-30
Our investigation shows that the Ginzubrg—Landau potential is somewhat too sensitive to work with in practice. The main reason for the increased sensitivity is non-convexity of the potential which leads to less robust numerical schemes. Instead, we discovered that functionals based on the elastic and membrane energies are much more robust and easier to work with. While both energy functionals can be used for similar applications, the elastic energy we developed is especially useful to handle non-smooth surfaces which contain sharp corners or edges. In addition, we demonstrated that our core method can be utilized on data that originate from complex dynamical systems such as fluid flows and weather systems. Thus, we developed a simple method for analyzing the behavior of such complex systems in terms of their dominating main modes and their decay and growth rates
The project terminates before term by the end of the outgoing phase.