Seminar in Numerical Analysis: Malte Peter (University of Augsburg)

Identification of microstructural information from macroscopic boundary measurements in linear elasticity

We consider the upscaled linear elasticity problem in the context of periodic homogenisation in the stationary setting as well as in the time-dependent regime where the wavelength is much larger than the microstructure. Based on measurements of the deformation of the (macroscopic) boundary of a body for a given forcing, the aim is to deduce information on the geometry of the microstructure. After a general introduction to periodic homogenisation in the context of linear elasticity, we are able to prove for a parametrised microstructure that there exists at least one solution of the associated minimisation problem based on the L^2-difference of the measured deformation and the computed deformation for a given parameter vector. To facilitate the use of gradient-based algorithms, we derive the Gâteaux derivatives using the Lagrangian method of Céa, and we present numerical experiments showcasing the functioning of the method.

This is joint work with T. Lochner (University of Augsburg).

For further information about the seminar, please visit this webpage.

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