dune-vem 2.11.dev20250116

Implementation of a number of virtual element spaces and bilinear forms

DUNE-VEM

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DUNE-VEM is a Distributed and Unified Numerics Environment module which provides implementation of a range of virtual element spaces. It is based on the interfaces defined in DUNE-FEM. In addition to the C++ implementation and extensive Python interface is provided.

If you need help, please ask on our mailinglist. Bugs can also be submitted to the DUNE-VEM bugtracker instead.

Paper

A detailed description of the VEM implementation is given in our paper A framework for implementing general virtual element spaces. Please cite this paper, if you find this module useful for your research.

The scripts to reproduce the numerical examples provided in the paper are provided in the dune-vem-paper repository. These were based on the 2.9.0 version of DUNE. Versions of these scripts updated to match the current versions together with some new ones are included in this repository and are part of the Python package uploaded to PyPi. To obtain the current versions of these scripts after installation of the DUNE-VEM Python package you can run

python -m dune.vem

which places the scripts into the folder vem_tutorial.

Tutorial

The more general DUNE-FEM tutorial includes a number of further examples showcasing the DUNE-VEM module and provides an overview of DUNE.

General installation instructions

Using pip

DUNE-VEM can be installed using the Package Index of Python (pip).

pip install dune-vem

See https://dune-project.org/doc/installation-pip/ for a more detailed description.

From source

For a full explanation of the DUNE installation process please read the installation notes.

When using the main branch observe the build status to make sure you get a working version.

Dependencies

DUNE-VEM requires a recent C++ compiler (e.g. g++ or clang), cmake, pkg-config (see DUNE installation for details) and depends on the following DUNE modules:

• dune-common

• dune-geometry

• dune-grid

• dune-fem

The following DUNE modules are suggested:

• dune-istl

• dune-localfunctions

• dune-alugrid

• dune-spgrid

The following software is optional:

• PETSc

• SIONlib

• SuiteSparse

License

The DUNE-VEM library, headers and test programs are free open-source software, licensed under version 2 or later of the GNU General Public License.

See the file LICENSE for full copying permissions.

References

A detailed description of DUNE-VEM and the uderlying DUNE-FEM module can be found in

• A. Dedner, A. Hodson. A framework for implementing general virtual * element space. https://arxiv.org/abs/2208.08978

• A. Dedner, R. Klöfkorn, M. Nolte, and M. Ohlberger. A Generic Interface for Parallel and Adaptive Scientific Computing: Abstraction Principles and the DUNE-FEM Module. Computing, 90(3-4):165--196, 2010. http://dx.doi.org/10.1007/s00607-010-0110-3

• A. Dedner, R. Klöfkorn, and M. Nolte. Python Bindings for the DUNE-FEM module. Zenodoo, 2020 http://dx.doi.org/10.5281/zenodo.3706994

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