Article

Topological Sensitivity Analysis for the Location of Small Cavities in Stokes Flow

SIAM Journal on Control and Optimization (Impact Factor: 1.39). 01/2009; 48(5):2871-2900. DOI: 10.1137/070704332
Source: DBLP

ABSTRACT The moulds' filling process may generate flaws consisting of small gas bubbles trapped inside the material, which weaken the solidity of the casted piece. We consider here the inverse problem of determining these small size flaws' locations from velocities boundary measurements. The fluid flow is described by a simplified model based on the Stokes system. A numerical algorithm based on the topological sensitivity analysis applied to an energy-like misfit functional is worked out to that end.

1 Follower
 · 
86 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This article concerns an extension of the topological sensitivity (TS) concept for 2D potential problems involving insulated cracks, whereby a misfit functional J is expanded in powers of the characteristic size a of a crack. Going beyond the standard TS, which evaluates (in the present context) the leading O(a2) approximation of J, the higher-order TS established here for a small crack of arbitrarily given location and shape embedded in a 2-D region of arbitrary shape and conductivity yields the O(a4) approximation of J. Simpler and more explicit versions of this formulation are obtained for a centrally symmetric crack and a straight crack. A simple approximate global procedure for crack identification, based on minimizing the O(a4) expansion of J over a dense search grid, is proposed and demonstrated on a synthetic numerical example. BIE formulations are prominently used in both the mathematical treatment leading to the O(a4) approximation of J and the subsequent numerical experiments.
    Engineering Analysis with Boundary Elements 02/2011; 35(2-35):223-235. DOI:10.1016/j.enganabound.2010.08.007 · 1.44 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This article is concerned with establishing the topological sensitivity (TS) against the nucleation of small trial inclusions of an energy-like cost function. The latter measures the discrepancy between two time-harmonic elastodynamic states (respectively defined, for cases where overdetermined boundary data is available for identification purposes, in terms of Dirichlet or Neumann boundary data for the same reference solid) as the strain energy of their difference. Such cost function constitutes a particular form of error in constitutive relation and may be used for e.g. defect identification. The TS is expressed in terms of four elastodynamic fields, namely the free and adjoint solutions for Dirichlet or Neumann data. A similar result is also given for the linear acoustic scalar case. A synthetic numerical example where the TS result is used for the qualitative identification of an inclusion is presented for a simple 2D acoustic configuration.
    Comptes Rendus Mecanique 07/2010; 338(7):377-389. DOI:10.1016/j.crme.2010.07.016 · 1.05 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of a constitutive law error functional. Several numerical experiments are conducted which show the efficiency of the method.