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UID:news1656@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20240415T160416
DTSTART;TZID=Europe/Zurich:20240426T110000
SUMMARY:Seminar in Numerical Analysis: Malte Peter (University of Augsburg)
DESCRIPTION:We consider the upscaled linear elasticity problem in the conte
 xt of periodic homogenisation in the stationary setting as well as in the 
 time-dependent regime where the wavelength is much larger than the microst
 ructure. Based on measurements of the deformation of the (macroscopic) bou
 ndary of a body for a given forcing\, the aim is to deduce information on 
 the geometry of the microstructure. After a general introduction to period
 ic homogenisation in the context of linear elasticity\, we are able to pro
 ve for a parametrised microstructure that there exists at least one soluti
 on of the associated minimisation problem based on the L^2-difference of t
 he measured deformation and the computed deformation for a given parameter
  vector. To facilitate the use of gradient-based algorithms\, we derive th
 e Gâteaux derivatives using the Lagrangian method of Céa\, and we presen
 t numerical experiments showcasing the functioning of the method.\\r\\nThi
 s is joint work with T. Lochner (University of Augsburg).\\r\\n\\r\\nFor f
 urther information about the seminar\, please visit this webpage [t3://pag
 e?uid=1115].
X-ALT-DESC:<p>We consider the upscaled linear elasticity problem in the con
 text of periodic homogenisation in the stationary setting as well as in th
 e time-dependent regime where the wavelength is much larger than the micro
 structure. Based on measurements of the deformation of the (macroscopic) b
 oundary of a body for a given forcing\, the aim is to deduce information o
 n the geometry of the microstructure. After a general introduction to peri
 odic homogenisation in the context of linear elasticity\, we are able to p
 rove for a parametrised microstructure that there exists at least one solu
 tion of the associated minimisation problem based on the L^2-difference of
  the measured deformation and the computed deformation for a given paramet
 er vector. To facilitate the use of gradient-based algorithms\, we derive 
 the Gâteaux derivatives using the Lagrangian method of Céa\, and we pres
 ent numerical experiments showcasing the functioning of the method.</p>\n<
 p>This is joint work with T. Lochner (University of Augsburg).</p>\n\n<p>F
 or further information about the seminar\, please visit this <a href="t3:/
 /page?uid=1115" title="Opens internal link in current window">webpage</a>.
 </p>
DTEND;TZID=Europe/Zurich:20240426T120000
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