Abstract
Domain Decomposition has been extensively studied as a tool for parallel computing. But in many cases the problem posed includes domain decomposition in its statement. For these the necessary numerical analysis is different because domain decomposition is not only at the discrete level but also on the continuous problem. Therefore non-matching grids for their numerical solutions is more natural, but requires new error estimates.
Our main purpose is to compute with the data of Virtual Reality. In this paper we shall review earlier works, including our own[9][10][11] and we shall present the project freefem3d.
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
Bernardi D., F. Hecht, K. Otsuka, O. Pironneau: freefem+, a finite element software to handle several meshes. Dowloadable from ftp://ftp.ann.jussieu.fr/pub/soft/pironneau/, 1999.
Burden G., Coiffe Ph.: Virtual Reality Technology, New York, Wiley 1994.
Ciariet P.G: The Finite Element Method, Prentice Hall, 1977.
Data Exploreur: IBM Corporation Thomas J. Watson Research Center/Hawthorne from http://www.dx.com, 1997.
Del Pino S., Heikkola E., Pironneau O., Toivanen J.: A finite element method for virtual reality data. C.R.A.S., June 2000.
Hartman J., Wernecke J.: “The VRML 2.0 Handbook” Addison-Wesley 1996.
Hecht F, Lions J.L., Pironneau O.: Domain Decomposition Algorithm for Computed Aided Design. (To appear in the anniversary book of Necas)
Hecht F., Pironneau O.: Multiple meshes and the implementation of freefem-+, INRIA report March, 1999. Also on the web at ftp://ftp.ann.jussieu.fr/pub/soft/pironneau.
Lions J.L., Pironneau O.: Algorithmes parallèles pour la solution de problèmes aux limites, C.R.A.S., 327, pp 947–352, Paris 1998.
Lions J.L., Pironneau O.: Domain decomposition methods for CAD. C.R.A.S., 328, pp 73–80, Paris 1999.
Lions J.L., Pironneau O.: Domain decomposition methods for CAD. C.R.A.S., 328, pp 73–80, Paris 1999.
Lions J.L., Pironneau O.: Non-Overlapping Domain Decomposition of Evolution Operators C.R.A.S. Paris June 2000.
Lions P.L.: On the Schwarz alternating method. I,II,III. Int Symposium on Domain decomposition Methods for Partial Differential Equations. SIAM, Philadelphia, 1988, 89, 90.
Pironneau O.: Finite Element Methods for Fluids Wiley, Chichester 1987.
Smith B., Bjørstad P., Gropp W.: Domain decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge, 1996.
Steger J.L.: The Chimera method of flow simulation, Workshop on applied CFD, Univ of Tennessee Space Institute, August 1991.
R. Suzuki R.: A patch to POV-Ray for iso-surfaces. In http://www.public.usit.net/rsuzuki/e/povray/iso/index.html.
Wardley A.: Persistence of Vision, POV-Ray in http://www.povray.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Delpino, S., Lions, J.L., Pironneau, O. (2002). A-priori Domain Decomposition of PDE Systems and Applications. In: Babuška, I., Ciarlet, P.G., Miyoshi, T. (eds) Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Lecture Notes in Computational Science and Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56288-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-56288-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42399-7
Online ISBN: 978-3-642-56288-4
eBook Packages: Springer Book Archive