dune-surfaces_int

Code to produce the results of the paper.

@article{...,
  title={High-order integration for regular cubical re-parameterizations of triangulated manifolds reaches super-algebraic approximation rates},
  author={Zavalani, G., Sander, O. and Hecht, M.},
  year={2023}
}

Preparing the Sources

This project is developed in the DUNE framework.

You need to install the following dependencies, all with the branch releases/2.7

• dune-common
• dune-geometry
• dune-localfunctions
• dune-istl
• dune-grid
• dune-typetree
• dune-functions
• dune-foamgrid
• dune-vtk
• dune-curvedgeometry
• dune-curvedgrid
• dune-gmsh4

Put all these modules together with this project into a common base directory, called my_dune in the following. This module is assumed to be in a subdirectory called dune-surface_int.

As additional external dependencies we have

• CMake >= 3.13
• PkgConfig
• SuiteSparse

that can be installed as packages in your Linux distribution.

Compiling the Code

If these preliminaries are met, you should run

cd my_dune
dunecontrol cmake -DCMAKE_BUILD_TYPE=Release
dunecontrol make

to configure and compile all modules, including this one. All CMake and make output is put into the build directory build-cmake/.

For further information about the installation process, see also the official documentation https://dune-project.org/doc/installation/ of DUNE.

Run the Examples from dune-surface_int

In order to execute the code to run the numerical examples for the biconcave shape, run

cd my_dune/dune-surface_int./build-cmake/src/biconcave_disc

for the double torus, run

cd my_dune/dune-surface_int./build-cmake/src/double_torus

for the genus two surface, run

cd my_dune/dune-surface_int./build-cmake/src/genus_surface