dunetpmc
dunetpmc
Provides a topology preserving implementation of the marching cubes and marching simplex algorithm. This module can be used to implement cutcell algorithms on top of the Dune interface.
Requires: 
dunecommon

Maintainer:  Christian Engwer, Andreas Nüßing 
Git repository: 
https://gitlab.duneproject.org/extensions/dunetpmc 
Given a scalar P1/Q1 function Φ on a domain Ω, we define a partition of Ω into two subdomains {Ω1, Ω2} with a common interface Γ. The interface is given as the zero levelset of the scalar function Φ. The marching cubes algorithm computes a piecewise linear reconstruction of Γ.
The dunemc modules not only computes a reconstruction of the interface, but also further information. The user can access the following information:
 Reconstruction of the interface Γ
 Reconstruction of Ω1
 Reconstruction of Ω2
 Connectivity pattern w.r.t. each subdomain
In order to allow the algorithm to be employed in Finite Element simulations, a reconstruction has to fullfill certain topological guarantees:
 The connectivity pattern of the cell vertices must be preserved within each subentity. In particular this means that vertices connected along an edge, face or volume, should still be connected via the same subentity.
 The exact interface Γ partitions each grid cell into patches belonging to either Ω1 or Ω2. We require that number of patches and their domain association is the same in the polygonal reconstruction.
 The vertices of the reconstructed interface lie on the exact zero levelset.
Publications and Documentation
The first concepts of dunemc are published in
P. Bastian, C. Engwer. An unfitted finite element method using discontinuous Galerkin. International Journal for Numerical Methods in Engineering, 79(12), 2009 , 15571576
 Ch. Engwer, An Unfitted Discontinuous Galerkin Scheme for Microscale Simulations and Numerical Upscaling, Heidelberg University, 2009. (PDF)
We are working on a more thorough publication which will also cover the improved Topology Preserving Marching Cubes Algorithm. A preprint is available from Arxiv:
 C. Engwer, A. Nüßing , Geometric Integration Over Irregular Domains with topologic Guarantees, 2016 (arXiv:1601.03597)
Maintainers
dunetpmc has been written by Christian Engwer and Andreas Nüßing.