A-priori Domain Decomposition of PDE Systems and Applications
Conference paper
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.
Keywords
Virtual Reality Domain Decomposition Quadrature Point Constructive Solid Geometry Fictitious Domain Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- 1.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.
- 2.Burden G., Coiffe Ph.: Virtual Reality Technology, New York, Wiley 1994.Google Scholar
- 3.Ciariet P.G: The Finite Element Method, Prentice Hall, 1977.Google Scholar
- 4.Data Exploreur: IBM Corporation Thomas J. Watson Research Center/Hawthorne from http://www.dx.com, 1997.
- 5.Del Pino S., Heikkola E., Pironneau O., Toivanen J.: A finite element method for virtual reality data. C.R.A.S., June 2000.Google Scholar
- 6.Hartman J., Wernecke J.: “The VRML 2.0 Handbook” Addison-Wesley 1996.Google Scholar
- 7.Hecht F, Lions J.L., Pironneau O.: Domain Decomposition Algorithm for Computed Aided Design. (To appear in the anniversary book of Necas)Google Scholar
- 8.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.
- 9.Lions J.L., Pironneau O.: Algorithmes parallèles pour la solution de problèmes aux limites, C.R.A.S., 327, pp 947–352, Paris 1998.MathSciNetMATHGoogle Scholar
- 10.Lions J.L., Pironneau O.: Domain decomposition methods for CAD. C.R.A.S., 328, pp 73–80, Paris 1999.MathSciNetMATHGoogle Scholar
- 11.Lions J.L., Pironneau O.: Domain decomposition methods for CAD. C.R.A.S., 328, pp 73–80, Paris 1999.MathSciNetMATHGoogle Scholar
- 12.Lions J.L., Pironneau O.: Non-Overlapping Domain Decomposition of Evolution Operators C.R.A.S. Paris June 2000.Google Scholar
- 13.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.Google Scholar
- 14.Pironneau O.: Finite Element Methods for Fluids Wiley, Chichester 1987.Google Scholar
- 15.Smith B., Bjørstad P., Gropp W.: Domain decomposition. Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge, 1996.Google Scholar
- 16.Steger J.L.: The Chimera method of flow simulation, Workshop on applied CFD, Univ of Tennessee Space Institute, August 1991.Google Scholar
- 17.R. Suzuki R.: A patch to POV-Ray for iso-surfaces. In http://www.public.usit.net/rsuzuki/e/povray/iso/index.html.
- 18.Wardley A.: Persistence of Vision, POV-Ray in http://www.povray.org
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