×

A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE. (English) Zbl 1151.65088

Summary: In part I [ibid. 82, No. 2–3, 103–119 (2008; Zbl 1151.65089)] we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structures. Thus, user implementations become independent of the underlying grid implementation. Modern C++ template techniques are used to provide an interface implementation without big performance losses. The implementation is realized as part of the software environment DUNE (http://dune-project.org/). Numerical tests demonstrate the flexibility and the efficiency of our approach.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Citations:

Zbl 1151.65089
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] ALUGrid Library. http://www.mathematik.uni-freiburg.de/IAM/Research/alugrid/
[2] Bangerth W (2000) Using modern features of C++ for adaptive finite element methods: Dimension-independent programming in deal II. In: Deville M, Owens R (eds). Proceedings of the 16th IMACS world congress 2000, Lausanne, Switzerland, 2000. Document Sessions/118-1
[3] Bastian P, Birken K, Johannsen K, Lang S, Neuss N, Rentz-Reichert H, Wieners C (1997) UG–A flexible software toolbox for solving partial differential equations. Comp Vis Sci 1: 27–40 · Zbl 0970.65129
[4] Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Ohlberger M, Sander O (2007) A generic grid interface for parallel and adaptive scientific computing. Part I. Abstract framework. Computing (this issue) (in preparation) · Zbl 1151.65089
[5] Bastian P, Droske M, Engwer C, Klöfkorn R, Neubauer T, Ohlberger M, Rumpf M (2004) Towards a unified framework for scientific computing. In: Kornhuber R, Hoppe R, Keyes D, Périaux J, Pironneau O, Xu J(eds) Proceedings of the 15th conference on domain decomposition methods, no 40 in LNCSE. Springer, Berlin, pp 167–174 · Zbl 1067.65103
[6] Blatt M, Bastian P (2006) The iterative solver template library. In: Proceedings of the workshop on state-of-the-art in scientific and parallel computing. Lecture notes in scientific computing. Springer, Berlin (accepted)
[7] Blatt M, Bastian P (2007) On the generic parallelisation of iterative solvers for the finite element method. Int J Comput Sci Eng (submitted)
[8] Burri A, Dedner A, Klöfkorn R, Ohlberger M (2005) An efficient implementation of an adaptive and parallel grid in DUNE. Technical report, Submitted to: Proceedings of the 2nd Russian-German advanced research workshop on computational science and high performance computing, Stuttgart, March 14–16
[9] Dedner A, Rohde C, Schupp B, Wesenberg M (2004) A parallel, load balanced MHD code on locally adapted, unstructured grids in 3D. Comp Vis Sci 7: 79–96 · Zbl 1120.76338
[10] DUNE–distributed and unified numerics environment. http://dune-project.org/
[11] Eck C (1996) Existenz und Regularität der Lösungen für Kontaktprobleme mit Reibung. PhD Thesis, Universität Stuttgart · Zbl 0867.73071
[12] Gamma E, Helm R, Johnson R, Vlissides J (1995) Design patterns: elements of reusable object-oriented software. Addison-Wesley, USA · Zbl 0887.68013
[13] Kornhuber R, Krause R, Sander O, Deuflhard P, Ertel S (2006) A monotone multigrid solver for two body contact problems in biomechanics. Comp Vis Sci (accepted for publication)
[14] Krause R, Sander O (2006) Automatic construction of boundary parametrizations for geometric multigrid solvers. Comp Vis Sci 9: 11–22 · Zbl 05027718
[15] Kröner D (1997) Numerical schemes for conservation laws. Wiley-Teubner, Stuttgart · Zbl 0872.76001
[16] Musser D, Derge G, Saini A (2001) STL tutorial and reference guide. Addison-Wesley, USA. ISBN 0-201-37923-6
[17] Pflaum C (2001) Expression templates for partial differential equations. Comp Vis Sci 4(1): 1–8 · Zbl 0996.65117
[18] Schmidt A, Siebert K (2005) Design of adaptive finite element software–the finite element toolbox ALBERTA. Springer, Berlin · Zbl 1068.65138
[19] Schupp B (1999) Entwicklung eines effizienten Verfahrens zur Simulation kompressibler Strömungen in 3D auf Parallelrechnern. PhD Thesis, Mathematische Fakultät, Universität Freiburg
[20] Seymour J (1996) Views–a C++ standard template library extension. http://www.zeta.org.au/\(\sim\)jon/STL/views/doc/views.html
[21] Sick J, Lumsdane A (2000) A modern framework for portable high-performance numerical linear algebra. In: Langtangen H, Bruaset A, Quak E(eds) Advances in software tools for scientific computing, vol 10. Lecture notes in computational science and engineering. Springer, Berlin, pp 1–56
[22] Stalling D, Westerhoff M, Hege H-C (2005) Amira: a highly interactive system for visual data analysis. In: Hansen C, Johnson C(eds) The visualization handbook, chap 38. Elsevier, Amsterdam, pp 749–767
[23] Vandevoorde D, Josuttis N (2003) C++ templates–the complete guide. Addison-Wesley, USA
[24] Veldhuizen T (1999) Techniques for scientific C++. Technical report. http://extreme.indiana.edu/\(\sim\)tveldhui/papers/techniques/
[25] Veldhuizen T (2000) Blitz++: the library that thinks it is a compiler. In: Langtangen H, Bruaset A, Quak E(eds) Advances in Software tools for scientific computing, vol 10. Lecture notes in computational science and engineering. Springer, Berlin, pp 57–87 · Zbl 0947.68515
[26] Visible Human Project. http://www.nlm.nih.gov/research/visible/visible_human.html
[27] Wohlmuth B, Krause R (2003) Monotone methods on nonmatching grids for nonlinear contact problems. SIAM J Sci Comp 25(1): 324–347 · Zbl 1163.65334
[28] Woodward P, Colella P (1984) The numerical simulation of two-dimensional fluid flow with strong shocks. J Comput Phys 54: 115–173 · Zbl 0573.76057
[29] Young R, MacPhedran I Internet finite element resources. http://homepage.usask.ca/\(\sim\)ijm451/finite/fe_resources/fe_resources.html
[30] Zienkiewicz O, Zhu J (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Math Eng 24: 337–357 · Zbl 0602.73063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.