[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.
[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. 01/2011;
[show abstract][hide abstract] ABSTRACT: The moulds filling process may generate flaws consisting in 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.
Proceedings of the 49th IEEE Conference on Decision and Control, CDC 2010, December 15-17, 2010, Atlanta, Georgia, USA; 01/2010
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