Non-Overlapping DDMs to Solve Flow in Heterogeneous Porous Media
For flow problems in multi-layered porous media, one can define a natural non-overlapping domain decomposition (DD). The simplest way to obtain DDMs is to distribute interface conditions (pressure and flux continuity) for each pair of adjacent subdomains and to use the Dirichlet-Neumann (D-N) algorithm. A different way is the use of two Robin conditions (RC) also distributed for each subdomain (Robin-Method). The main inconvenience of both methods is that the convergence is not ensured. To obtain efficient methods, we retain from previous works two basic ideas: an acceleration of Aitken type for the D-N algorithm and finding optimized coefficients for the Robin-Method. In the present paper, we analyze these improved algorithms in 1-D and 2-D framework for flow problems in heterogeneous porous media and we present a numerical comparison.
KeywordsInterface Condition Domain Decomposition Domain Decomposition Method Heterogeneous Porous Medium Common Interface
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- D.-G. Calugaru, J.-M. Crolet, A. Chambaudet, and F. Jacob. Radon transport as an indicator of seismic activity. An algorithm for inverse problems. Computational Methods in Water Ressources, 47:631–638, 2002.Google Scholar
- B. Després, P. Joly, and J. E. Roberts. A domain decomposition method for the harmonic Maxwell equations. In Iterative methods in linear algebra (Brussels, 1991), pages 475–484, Amsterdam, 1992. North-Holland.Google Scholar
- I. Faille, E. Flauraud, F. Nataf, F. Schneider, and F. Willien. Optimized interface conditions for sedimentary basin modeling. In N. Debit et al., editor, Proc. of the 13th Int. Conf. on DDM, pages 461–468, 2001.Google Scholar
- F. Nataf, F. Rogier, and E. de Sturler. Optimal interface conditions for domain decomposition methods. Technical Report 301, CMAP, 1994.Google Scholar