In the numerical simulation of electro-magneto-mechanical devices,
the precise knowledge of certain material parameters is essential.
This talk deals with the problem of extracting these material parameters from
measured data, illustrated by applications in nonlinear magnetics and in
piezoelectricity. So far, quite complicated and costly experiments are done
in order to obtain the desired material data. We propose an approach using simple
measurements and applying more sophisticated mathematical algorithms, instead.
The resulting formulation of the parameter identification problem involves
the solution of PDEs, and the inverse problem is nonlinear and ill-posed in
the sense of unstable dependence of a solution on the data. For its stable
solution, we use fast forward solvers for the respective field problem, and
apply a Newton type regularization method with an appropriate stopping
criterion, using regularization by multilevel discretization in each Newton
step. In this context, multigrid methods for unstable problems provide
very efficient solvers especially for parameter identification
problems in PDEs.
Finally, numerical results are shown, and applicability to other parameter
identification problems is discussed.
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