Abstract
Overlapping domain decomposition methods are efficient and flexible. It is also important that such methods are inherently suitable for parallel computing. In this chapter, we will first explain the mathematical formulation and algorithmic composition of the overlapping domain decomposition methods. Afterwards, we will focus on a generic implementation framework and its applications within Diffpack.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. M. Bruaset, X. Cai, H. P. Langtangen, and A. Tveito. Numerical solution of PDEs on parallel computers utilizing sequential simulators. In Y. Ishikawa et al., editor, Scientific Computing in Object-Oriented Parallel Environment, Springer-Verlag Lecture Notes in Computer Science 1343, pages 161–168. Springer-Verlag, 1997.
X. Cai, E. Acklam, H. P. Langtangen, and A. Tveito. Parallel computing in Diffpack. In H. P. Langtangen and A. Tveito], editors, Advanced Topics in Computational Partial Differential Equations-Numerical Methods and Diffpack Programming. Springer, 20
T. F. Chan and T. P. Mathew. Domain decomposition algorithms. In Acta Numerica 1994, pages 61–143. Cambridge University Press, 1994.
C. Farhat and M. Lesoinne. Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Internat. J. Numer. Meth. Engrg., 36:745–764, 1993.
W. Hackbusch. Multigrid Methods and Applications. Springer, Berlin, 1985.
K.-A. Mardal, H. P. Langtangen, and G. Zumbusch. Multigrid methods. In H. P. Langtangen and A. Tveito, editors, Advanced Topics in Computational Partial Differential Equations-Numerical Methods and Diffpack Programming. Springer, 2003.
H. A. Schwarz. Gesammelte Mathematische Abhandlungen, volume 2, pages 133–143. Springer, Berlin, 1890. First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, volume 15, 1870, pp. 272-286.
B. F. Smith, P. E. Bjørstad, and W. Gropp. Domain Decomposition: Paral-lel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.
D. Vanderstraeten and R. Keunings. Optimized partitioning of unstructured finite element meshes. Internat. J. Numer. Meth. Engrg., 38:433–450, 1995.
J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34(4):581–613, December 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cai, X. (2003). Overlapping Domain Decomposition Methods. In: Langtangen, H.P., Tveito, A. (eds) Advanced Topics in Computational Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18237-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-18237-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-01438-6
Online ISBN: 978-3-642-18237-2
eBook Packages: Springer Book Archive