A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the Dune-Fem module

Computing (Vienna/New York)

Volumn 90, Issue 3-4, 2010, Pages 165-196

  Dedner, Andreas ^a   Klöfkorn, Robert ^a   Nolte, Martin ^a   Ohlberger, Mario ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Abstract interface; Adaptive methods; C++; Discontinuous Galerkin; DUNE; Dynamic load balancing; Finite elements; Finite volumes; Generic programming; Parallelization; Partial differential equations; Software

Indexed keywords

ABSTRACT INTERFACES; ADAPTIVE METHODS; C++; DISCONTINUOUS GALERKIN; DUNE; DYNAMIC LOAD BALANCING; FINITE ELEMENT; FINITE VOLUME; GENERIC PROGRAMMING; PARALLELIZATIONS; PARTIAL DIFFERENTIAL; SOFTWARE;

ABSTRACTING; BENCHMARKING; COMPUTER SOFTWARE; DATA STRUCTURES; DYNAMIC LOADS; FINITE VOLUME METHOD; FUNCTIONS; GALERKIN METHODS; MATHEMATICAL OPERATORS; PARALLEL ARCHITECTURES; PARTIAL DIFFERENTIAL EQUATIONS;

OBJECT ORIENTED PROGRAMMING;

EID: 78650605818     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-010-0110-3     Document Type: Article

References (33)

1. Y Abdelaziz A Hamouine 2008 A survey of the extended finite element Comput Struct 86 11-12 1141 1151 10.1016/j.compstruc.2007.11.001
2. DN Arnold F Brezzi B Cockburn LD Marini 2002 Unified analysis of discontinuous Galerkin methods for elliptic problems SIAM J Numer Anal 39 5 1749 1779 1008.65080 10.1137/S0036142901384162 1885715 (Pubitemid 35324903)
3. Bangerth W, Hartmann R, Kanschat G (2007) deal.II-a general-purpose object-oriented finite element library. ACM Trans Math Softw 33(4):24, 27
4. P Bastian K Birken K Johannsen S Lang N Neuss H Rentz-Reichert C Wieners 1997 UG-a flexible software toolbox for solving partial differential equations Comput Visual Sci 1 27 40 0970.65129 10.1007/s007910050003
5. P Bastian M Blatt A Dedner C Engwer R Klöfkorn R Kornhuber M Ohlberger O Sander 2008 A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in dune Computing 82 2-3 121 138 1151.65088 10.1007/s00607-008-0004-9 2421580
6. P Bastian M Blatt A Dedner C Engwer R Klöfkorn M Ohlberger O Sander 2008 A generic grid interface for parallel and adaptive scientific computing. I: Abstract framework Computing 82 2-3 103 119 1151.65089 10.1007/s00607-008-0003- x 2421579
7. Blatt M, Bastian P (2007) The iterative solver template library. In: Kagström B, Elmroth E, Dongarra J, Wasniewski J (eds) Applied parallel computing-state of the art in scientific computing. Springer, Berlin, pp 666-675
8. Brenner SC, Ridgway Scott L (2008) The mathematical theory of finite element methods. In: Texts in applied mathematics, 3rd edn, vol 15. Springer, New York
9. Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, Berlin
10. Burri A, Dedner A, Diehl D, Klöfkorn R, Ohlberger M (2006) A general object oriented framework for discretizing nonlinear evolution equations. In: Shokin YI, Resch M, Danaev N, Orunkhanov M, Shokina N (eds) Advances in high performance computing and computational sciences. Notes on numerical fluid mechanics and multidiciplinary design (NNFM), vol 93. Springer, Berlin
11. Burri A, Dedner A, Klöfkorn R, Ohlberger M (2006) An efficient implementation of an adaptive and parallel grid in dune. In: Krause E, Shokin YI, Resch M, Shokina N (eds) Advances in high performance computing and computational sciences. Notes on numerical fluid mechanics adn multidisciplinary design (NNFM), vol 91. Springer, Berlin
12. P Castillo R Rieben D White 2005 FEMSTER: an object-oriented class library of high-order discrete differential forms ACM Trans Math Softw 31 4 425 457 1136.78330 10.1145/1114268.1114269 2272340
13. Ciarlet PG (1987) The finite element methods for elliptic problems. North-Holland, Amsterdam
14. B Cockburn C-W Shu 2001 Runge-Kutta discontinuous Galerkin methods for convection-dominated problems J Sci Comput 16 3 173 261 1065.76135 10.1023/A:1012873910884 1873283 (Pubitemid 33818237)
15. TA Davis 2004 Algorithm 832: UMFPACK v4.3-an unsymmetric-pattern multifrontal method ACM Trans Math Softw 30 2 196 199 1072.65037 10.1145/992200.992206
16. Dedner A, Klöfkorn R (2008) A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems. Preprint no. 8. Submitted to SIAM Sci. Comput. Mathematisches Institut, Unversität Freiburg. http://www.mathematik.uni-freiburg.de/IAM/homepages/ robertk/postscript/dedner-kloefkorn-limiter.pdf
17. Dedner A, Luethi M, Albrecht T, Vetter T (2007) Curvature guided level set registration using adaptive finite elements. In: Hamprecht F, Schnorr C, Jahne B (eds) Proceedings of the 29th annual symposium of the German association for pattern recognition. Springer, Berlin
18. A Dedner C Rohde B Schupp M Wesenberg 2004 A parallel, load balanced mhd code on locally adapted, unstructured grids in 3d Comput Visual Sci 7 79 96 1120.76338 10.1007/s00791-004-0140-5 2088784
19. Diehl D (2007) Higher order schemes for simulation of compressible liquid-vapor flows with phase change. PhD thesis, Universität Freiburg. http://www.freidok.uni-freiburg.de/volltexte/3762/
20. Dune Fem Dune-Fem-The FEM Module. http://dune.mathematik.uni-freiburg.de/
21. Eymard R, Galluoët T, Herbin R (2000) Finite volume methods. In: Handbook of numerical analysis, vol VII. North-Holland, Amsterdam, pp 713-1020
22. J-F Gerbeau B Perthame 2001 Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation Discrete Contin Dyn Syst Ser B 1 1 89 102 0997.76023 10.3934/dcdsb.2001.1.89 1821555
23. Gersbacher C (2008) Local Discontiunous Galerkin Verfahren zur Simulation flacher dreidimensionaler Strömungen mit freier Oberfläche. Diploma thesis, Universität Freiburg
24. B Haasdonk M Ohlberger 2008 Reduced basis method for finite volume approximations of parametrized linear evolution equations M2AN Math Model Numer Anal 42 2 277 302 05262088 10.1051/m2an:2008001 2405149
25. Henning P, Ohlberger M (2009) Advection diffusion problems with rapidly oscillating coefficients and large expected drift. Part 2: The heterogeneous multiscale finite element method. Technical report, University of Münster (to be submitted)
26. G Karypis V Kumar 1999 A fast and highly quality multilevel scheme for partitioning irregular graphs SIAM J Sci Comput 20 1 359 392 0915.68129 10.1137/S1064827595287997 1639073
27. G Karypis V Kumar 1999 Multilevel k-way partitioning scheme for irregular graphs SIAM Rev 41 2 278 300 0918.68073 10.1137/S0036144598334138 1684545
28. Kröner D (1997) Numerical schemes for conservation laws. Wiley, Stuttgart
29. Lehn ML (2008) FLENS A flexible library for efficient numerical solutions. PhD thesis, Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm. http://flens.sourceforge.net/
30. Leveque RJ (2002) Finite volume methods for hyperbolic problems. In: Cambridge texts in applied mathematics. Cambridge University Press, Cambridge
31. Patera AT, Rozza G (2007) Reduced Basis approximation and a posteriori error estimation for parametrized partial differential equations. MIT, Version 1.0, Copyright MIT 2006-2007. In: (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering (to appear)
32. Schmidt A, Siebert KG (2005) Design of adaptive finite element software-the finite element toolbox ALBERTA. Springer, Berlin
33. Veldhuizen T The object-oriented numerics page. http://www.oonumerics. org/oon/