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A Non Overlapping Domain Decomposition Method for the Obstacle Problem

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Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

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Abstract

We present a non-overlapping domain decomposition method for the obstacle problem. In this approach, the original problem is reformulated into two subproblems such that the first problem is a variational inequality in subdomain Ω i and the other is a variational equality in the complementary subdomain Ω e, where Ω e and Ω i are multiply-connected, in general. The main challenge is to obtain the global solution through coupling of the two subdomain solutions, which requires the solution of a nonlinear interface problem. This is achieved via a fixed point iteration. This new formulation reduces the computational cost as the variational inequality is solved in a smaller region. The algorithm requires some mild assumption about the location of Ω i, which is the domain containing the region corresponding to the coincidence set. Numerical experiments are included to illustrate the performance of the resulting method.

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Authors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Samia Riaz & Daniel Loghin

  2. UET, Lahore, Pakistan

    Samia Riaz

Authors
  1. Samia Riaz
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  2. Daniel Loghin
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Corresponding author

Correspondence to Daniel Loghin .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Géometrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. INRIA, Rennes, France

    Géraldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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Riaz, S., Loghin, D. (2014). A Non Overlapping Domain Decomposition Method for the Obstacle Problem. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_85

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