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 dunetpmc 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
If you are using the dunetpmc module, please cite
C. Engwer, A. Nüßing. Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees. ACM Transactions on Mathematical Software, 44(2), 2018 , 120
(arXiv preprint arXiv:1601.03597)
The first concepts of dunetpmc go back to implementations described 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)
Installation
dunetpmc depends on the TPMC
library for generating of the lookuptables.
You can install TPMC
via
pip
. Currently it is not listed in
the pypi
repository and must be installed directly from the github repository:
 for python 2:
> python m pip install git+https://github.com/tpmc/tpmc.git
 for python 3 we have preliminary support:
> python m pip install git+https://github.com/tpmc/tpmc.git@python3
Maintainers
dunetpmc has been written by Christian Engwer and Andreas Nüßing.