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January 2022
A voir
2011-GdT ITER - Y. Fischer
Intervention de Yannick Fischer
Title
Approximation methods for inverse elliptic problems and applications to tokamaks
Abstract
This talk is concerned with the Cauchy problem which consists in
recovering Dirichlet and Neumann data on a part of the boundary of a
bounded open planar domain from their knowledge on the complementary
part. The unknown quantity is governed by a real elliptic equation with
a smooth diffusion coefficent.
The first part of this talk deals with the fact that the inverse problem
for elliptic diffusion equation we have in mind may be expressed as a
best approximation problem under constraint for the complex conjugated
Beltrami equation. Such a technique has already proved its relevance for
harmonic identification of linear control systems from partial frequency
data.
Another important practical motivation comes from plasma confinement in
tokamak. A constructive method supported by the use of an appropriate
basis of functions is proposed and gives rise to a robust algorithm for
identifying the plasma shape. Some numerical simulations illustrates the
efficiency of the method.