Welcome to the dune-fem tutorial (for version 2.10)

This module brings python scripting support to Dune. This version describes the bindings for the development version (to become 2.10). The bindings serves three purposes:

  1. High level program control for solving partial differential equations using classes from the Dune core and from Dune-Fem [BBD+08, DKNO10] with a recent update provided in [BBD+21]. The unified form language UFL [ALO+13] is used to describe the mathematical model, all realizations of the Dune grid interface can be used to work with the domain tessellation, and the finite element spaces, operator, and solvers provided by Dune-Fem for the discretizations and solving steps. All of this is available to be used in python scripts or through Jupyter notebooks.

  2. Rapid prototyping of new methods or other parts of a simulation is easy since the interfaces provided are very similar to the Dune C++ interface. This makes it easy to transfer a working prototype from python (easy to develop) to C++ (high efficiency). Small C++ code snippets can be easy called from python using just in time compilation.

  3. Rapid prototyping of new implementations of Dune interfaces. For example new implementations of the Dune grid interface can be easily tested. For Dune-Fem developers, new grid views, discrete function spaces, and scheme classes can be added and tested.

Table of Content

Bibliography

AGL05

James Ahrens, Berk Geveci, and Charles Law. Paraview: an end-user tool for large data visualization. The visualization handbook, 2005. URL: https://www.paraview.org.

ALO+13

M. Alnaes, A. Logg, K. Olgaard, M. Rognes, and G. Wells. A Unified Form Language: A domain-specific language for weak formulations of partial differential equations. 2013. URL: https://arxiv.org/abs/1211.4047.

APFC17

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BAA+18

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BBD+08

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and O. Sander. A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part II: Implementation and Tests in DUNE. Computing, 82(2–3):121–138, 2008. doi:10.1007/s00607-008-0004-9.

BBD+21

P. Bastian, M. Blatt, M. Dedner, N.-A. Dreier, R. Engwer, Ch. Fritze, C. Gräser, Ch. Grüninger, D. Kempf, R. Klöfkorn, M. Ohlberger, and O. Sander. The Dune framework: Basic concepts and recent developments. CAMWA, 2021. doi:10.1016/j.camwa.2020.06.007.

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Markus Blatt and Peter Bastian. The iterative solver template library. In International Workshop on Applied Parallel Computing, 666–675. Springer, 2006.

BDK12

S. Brdar, A. Dedner, and R. Klöfkorn. Compact and stable Discontinuous Galerkin methods for convection-diffusion problems. SIAM J. Sci. Comput., 34(1):263–282, 2012. doi:10.1137/100817528.

DPKC11

Lisandro D Dalcin, Rodrigo R Paz, Pablo A Kler, and Alejandro Cosimo. Parallel distributed computing using python. Advances in Water Resources, 34(9):1124–1139, 2011. doi:10.1016/j.advwatres.2011.04.013.

DDE05

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DH21

A. Dedner and A. Hodson. Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients. IMA Journal of Numerical Analysis, :, 2021. doi:10.1093/imanum/drab003.

DKKN18

A. Dedner, B. Kane, R. Klöfkorn, and M. Nolte. Python framework for hp adaptive discontinuous galerkin methods for two-phase flow in porous media. Applied Mathematical Modelling, 67:, 10 2018. doi:10.1016/j.apm.2018.10.013.

DK21

A. Dedner and R. Klöfkorn. Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method. Commun. Appl. Math. Comput., 2021. doi:10.1007/s42967-021-00134-5.

DKNO10

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. doi:10.1007/s00607-010-0110-3.

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JOP+--

Eric Jones, Travis Oliphant, Pearu Peterson, and others. SciPy: open source scientific tools for Python. 2001–. URL: http://www.scipy.org/.

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T. Kieu. Galerkin Finite Element Method for Generalized Forchheimer Equation of Slightly Compressible Fluids in Porous Media. 2015. URL: https://arxiv.org/abs/1508.00294.

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WRM17

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