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Using Self-adjoint Extensions in Shape Optimization

  • Antoine Laurain
  • Katarzyna Szulc
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 312)

Abstract

Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriate self-adjoint extension of the Laplacian, according to the previous asymptotic analysis. The sensitivity with respect to the position of the center of the small hole is then studied for a class of functionals depending on the domain. A numerical application for solving an inverse problem is presented. Error estimates are provided and a link to the notion of topological derivative is established.

Keywords

Asymptotic Analysis Elliptic Operator Small Hole Shape Optimization Singular Perturbation 
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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Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Antoine Laurain
    • 1
  • Katarzyna Szulc
    • 2
  1. 1.Department of Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  2. 2.Institut Élie CartanUniversity Henri PoincaréNancy1France

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