Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)

Peter Bastian; Felix Heimann; Sven Marnach

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 294-315
  • ISSN: 0023-5954

Abstract

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In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying polynomial degree. The underlying Dune software framework provides parallelization and dimension-independence.

How to cite

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Bastian, Peter, Heimann, Felix, and Marnach, Sven. "Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)." Kybernetika 46.2 (2010): 294-315. <http://eudml.org/doc/197255>.

@article{Bastian2010,
abstract = {In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying polynomial degree. The underlying Dune software framework provides parallelization and dimension-independence.},
author = {Bastian, Peter, Heimann, Felix, Marnach, Sven},
journal = {Kybernetika},
keywords = {finite elements; generic programming; finite elements; generic programming; finite volume method; discontinuous Galerkin method; heat equation; numerical examples; second order elliptic equation; distributed and unified numerics environment; essential boundary conditions; hanging nodes; parallelization},
language = {eng},
number = {2},
pages = {294-315},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)},
url = {http://eudml.org/doc/197255},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Bastian, Peter
AU - Heimann, Felix
AU - Marnach, Sven
TI - Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 294
EP - 315
AB - In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying polynomial degree. The underlying Dune software framework provides parallelization and dimension-independence.
LA - eng
KW - finite elements; generic programming; finite elements; generic programming; finite volume method; discontinuous Galerkin method; heat equation; numerical examples; second order elliptic equation; distributed and unified numerics environment; essential boundary conditions; hanging nodes; parallelization
UR - http://eudml.org/doc/197255
ER -

References

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  3. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O., A generic grid interface for parallel and adaptive scientific computing, Part II: Implementation and tests in DUNE. Computing 82 (2008), 2-3, 121–138. MR2421580
  4. Blatt, M., Bastian, P., The iterative solver template library, In: Applied Parallel Computing. State of the Art in Scientific Computing (B. Kagstrüm, E. Elmroth, J. Dongarra, and J. Wasniewski, eds.) (Lecture Notes in Sci. Comput. 4699.) Spinger, Berlin 2007, pp. 666–675. 
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