Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface framework. Utilizing an adaptive finite element implementation with effective gradient recovery techniques, we discuss how the Euler number can be accurately computed directly from the numerically solved phase field functions or order parameters. Numerical examples and applications to the topological analysis of point clouds are also presented.