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On the Efficient Implementation of Multilevel Adaptive Methods

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Modern Software Tools for Scientific Computing

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Abstract

Adaptive multilevel methods are difficult to implement, because their basic software components are strongly interrelated and thus the modularization is nontrivial. Program design is further complicated by efficiency considerations. These issues are addressed in the abstract mesh concept and its implementation in a patch-adaptive multigrid program.

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References

  1. S. Balay, W. Gropp, L. C. McInnes, and B. F. Smith. Efficient management of parallelism in object-oriented numerical software libraries. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools for Scientific Computing, pages 163–202. Birkhäuser, 1997.

    Chapter  Google Scholar 

  2. R. E. Bank. PLTMG: A Software Package for Solving Elliptic Partial Differential Equations?Users? Guide 6.0, volume 7 of Frontiers in Applied Mathematics. SIAM Books, Philadelphia, 1990.

    Google Scholar 

  3. R. Beck, B. Erdman, and R. Roitzsch. An object-oriented adaptive finite element code: Design issues and applications in hyperthermia treatment planning. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools for Scientific Computing, pages 105–124. Birkhäuser, 1997.

    Chapter  Google Scholar 

  4. A. Brandt. Multi-level adaptive solutions to boundary value problems. Math. Corp., 31:333–390, 1977.

    Article  MATH  Google Scholar 

  5. A. M. Bruaset, E. Holm, and H. P. Langtangen. Increasing the efficiency and reliability of software development for systems of PDEs. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools for Scientific Computing, pages 247–268. Birkhäuser, 1997.

    Chapter  Google Scholar 

  6. D. C. Burger, J. R. Goodman, and A. Kägi. On the declining effectiveness of dynamic caching for general-purpose microprocessors. Technical Report CS-TR-95–1261, Computer Science Department, Univ. of Wisconsion-Madison, 1995.

    Google Scholar 

  7. H. Foerster and K. Witsch. Multigrid software for the solution of elliptic problems on rectangular domains: MG00 (Release 1). In W. Hackbusch and U. Trottenberg, editors, Multigrid Methods, volume 960 of Lecture Notes in Mathematics, pages 427–460, Berlin, 1982. Springer-Verlag.

    Google Scholar 

  8. W. Hackbusch. Multigrid Methods and Applications. Springer Verlag, Berlin, 1985.

    Google Scholar 

  9. C. R. Jänsch, U. Rüde and K. Schnepper. Macro expansion, a tool for the systematic development of scientific software. Bericht I-8814, Institut für Informatik, TU München, November 1988.

    Google Scholar 

  10. H. Lötzbeyer. Objektorientierte parallele adaptive Mehrgitterverfahren auf semistrukturierten Gittern. Dimplomarbeit, Insitut für Informatik, TU München, 1996.

    Google Scholar 

  11. H. Lötzbeyer and U. Rüde. Patch-adaptive multilevel iteration, 1996. Submitted to BIT, also available from mgnet: http://casper.cs.yale.edu/mgnet/www/mgnet.html.

    Google Scholar 

  12. S. F. McCormick. Multilevel Adaptive Methods for Partial Dijf`’erential Equations, volume 6 of Frontiers in Applied Mathematics. SIAM, Philadelphia, 1989.

    Book  Google Scholar 

  13. U. Rüde. Mathematical and computational techniques for multilevel adaptive methods, volume 13 of Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, USA, 1993.

    Book  Google Scholar 

  14. U. Rüde. On the V-cycle of the fully adaptive multigrid method. In W. Hackbusch and G. Wittum, editors, Adaptive methods — algorithms, theory and applications, Proceedings of the Ninth GAMM Seminar Kiel,Jan. 22–24, 1993, volume 46 of Notes on Numerical Fluid Dynamics, pages 251–260, Braunschweig, Wiesbaden, 1994. Vieweg.

    Google Scholar 

  15. T. Veldhuizen. Expression templates. C++ report, 7(5):26–31, June 1995.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Augsburg, Universitätsstrasse 14, D86159, Augsburg, Germany

    U. Rüde

Authors
  1. U. Rüde
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Editor information

Editors and Affiliations

  1. SINTEF Applied Mathematics, Blindern, N-0314, Oslo, Norway

    Erlend Arge  & Are Magnus Bruaset  & 

  2. University of Oslo, N-0316, Oslo, Norway

    Hans Petter Langtangen

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© 1997 Springer Science+Business Media New York

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Rüde, U. (1997). On the Efficient Implementation of Multilevel Adaptive Methods. In: Arge, E., Bruaset, A.M., Langtangen, H.P. (eds) Modern Software Tools for Scientific Computing. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1986-6_6

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  • DOI: https://doi.org/10.1007/978-1-4612-1986-6_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7368-4

  • Online ISBN: 978-1-4612-1986-6

  • eBook Packages: Springer Book Archive

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