Geodesic
Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)
Kybernetika, Tome 46 (2010) no. 2, pp. 294-315 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 35J25, 65M02, 65M60, 65N02, 65N30, 65Y02
Keywords: finite elements; generic programming 
@article{KYB_2010_46_2_a5,
     author = {Bastian, Peter and Heimann, Felix and Marnach, Sven},
     title = {Generic implementation of finite element methods in the {Distributed} and {Unified} {Numerics} {Environment} {(DUNE)}},
     journal = {Kybernetika},
     pages = {294--315},
     year = {2010},
     volume = {46},
     number = {2},
     mrnumber = {2663602},
     zbl = {1195.65130},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_2_a5/}
}
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
SP  - 294
EP  - 315
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2010_46_2_a5/
LA  - en
ID  - KYB_2010_46_2_a5
ER  - 
%0 Journal Article
%A Bastian, Peter
%A Heimann, Felix
%A Marnach, Sven
%T Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)
%J Kybernetika
%D 2010
%P 294-315
%V 46
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2010_46_2_a5/
%G en
%F KYB_2010_46_2_a5
Bastian, Peter; Heimann, Felix; Marnach, Sven. Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE). Kybernetika, Tome 46 (2010) no. 2, pp. 294-315. http://geodesic.mathdoc.fr/item/KYB_2010_46_2_a5/

[1] Bastian, P., Blatt, M.: On the generic parallelisation of iterative solvers for the finite element method. Internat. J. Comput. Sci. Engrg. 4 (2008), 1, 56–69.

[2] Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework. Computing 82 (2008), 2-3, 103–119. | MR

[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. | MR

[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.

[5] Bramble, J. H., Pasciak, J. E., Xu, J.: Parallel multilevel preconditioners. Math. Comput. 55 (1990), 1–22. | DOI | MR | Zbl

[6] Brezzi, F., Lipnikov, K., Simoncini, V.: A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Models and Methods in Applied Sciences 15 (2005), 10, 1533–1551. | DOI | MR | Zbl

[7] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems. SIAM, Philadelphia 2002. | MR | Zbl

[8] Dedner, A., Klöfkorn, R., Nolte, M., Ohlberger, M.: A generic interface for parallel and adaptive scientific computing: Abstraction principles and the Dune-Fem module. Preprint No. 3, Mathematisches Institut, Universität Freiburg, 2009. Submitted to Transactions on Mathematical Software.

[9] http://www.dune-project.org/, Dune Homepage, link visited August 3, 2009.

[10] Geuzaine, C., Remacle, J.-F.: Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities. Internat. J. Num. Methods in Eng., 2009. http://www.geuz.org/gmsh/, link visited August 3, 2009. | MR | Zbl

[11] Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface – A Contribution to the Modeling of Hydrosystems. Springer–Verlag, 1997.

[12] Oden, J. T., Babuška, I., Baumann, C. E.: A discontinuous hp finite element method for diffusion problems. J. Comput. Phys. 146 (1998), 491–519. | DOI | MR

[13] http://www.opencascade.com/, link visited August 3, 2009.

[14] http://www.paraview.org/, link visited August 3, 2009.

[15] http://www.mcs.anl.gov/petsc/petsc-as/, link visited August 5, 2009.

[16] http://www.salome-platform.org/, link visited August 3, 2009.

[17] http://trilinos.sandia.gov/, link visited August 5, 2009.

[18] Vandevoorde, D., Josuttis, N. M.: C++ Templates – The Complete Guide. Addison-Wesley, 2003.