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A Domain Decomposition Technique Applied to a Free Surface Seepage Problem

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Numerical Methods for Free Boundary Problems

Abstract

A domain decomposition technique for a free boundary seepage problem of flow through a porous dam with a toe drain is considered. An iterative procedure is proposed that reduces the problem to a sequence of problems on each subdomain, one which includes the free boundary and is described by a variational inequality and the other which includes the remainder of the problem and is described by a second-order elliptic equation. A relaxation is performed at the subdomain interfaces at each iteration. Numerical results are presented.

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References

  1. C. Baiocchi.: Free boundary problems in the theory of fluid flow through porous media. In Proc. Int. Congr. Math., pages 237–243, Vancouver, 1975.

    Google Scholar 

  2. J. Crank.: Free and Moving Boundary Problems. Clarendon Press, Oxford, England, 1984.

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  3. D. Funaro, A. Quarteroni, and P. Zanolli.: An iterative procedure with interface relaxation for domain decomposition methods. SIAM J. Numer. Anal., 25: 1213–1236, 1988.

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  4. M.E. Harr.: Groundwater and Seepage. McGraw-Hill, New York, 1962.

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  5. L.D. Marini and A. Quarteroni.: An iterative procedure for domain decomposition methods: a finite element approach. In R. Glowinski, G.H Golub, and J. Periaux, editors, Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1988.

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  6. L.D. Marini and A. Quarteroni.: A relaxation procedure for domain decomposition methods using finite elements. Numer. Math, 55: 575–598, 1989.

    Article  Google Scholar 

  7. J. M. Sloss and J.C. Bruch Jr.: Free surface seepage problems. J. Eng. Mech Div. Proc., ASCE 104, EM5: 1099–1111, 1978.

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© 1991 Springer Basel AG

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Papadopoulos, C.A., Sloss, J.M., Bruch, J.C. (1991). A Domain Decomposition Technique Applied to a Free Surface Seepage Problem. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_30

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  • DOI: https://doi.org/10.1007/978-3-0348-5715-4_30

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5717-8

  • Online ISBN: 978-3-0348-5715-4

  • eBook Packages: Springer Book Archive

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