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DTSTAMP:20230110T130741Z
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DTSTART;TZID=Europe/Berlin:20230119T141500
DTEND;TZID=Europe/Berlin:20230119T151500
SUMMARY:Oberseminar Analysis - Dr. Nicolas Clozeau (IST Austria)
DESCRIPTION:Title: Artificial Boundary Conditions for Random Elliptic Systems with Correlated Coefficient Field\n\nAbstract:\n\nIn this talk\, we are interested in numerical algorithms for computing the electrical field generated by a charge distribution localised on scale l in an infinite heterogeneous correlated random medium\, in a situation where the medium is only known in a box of diameter L>>l around the support of the charge. We study an artificial boundary condition recently introduced by Otto\, Lu and Wang suggesting optimal Dirichlet boundary conditions motivated by a multipole expansions established by Bella\, Giunti and Otto. Previously showed to be optimal in random media having a finite range of dependence\, we study here the effect of correlations on the algorithm. The correlations are encoded via a multi-scale spectral gap inequality which allow\, for instance\, to consider models of Gaussian fields with fat tails or various point processes such as Poisson tessellations and random parking which do not satisfy a finite range of dependence. With overwhelming probability\, we obtain a (near) optimal convergence rate with respect to scaling in terms of l\, L and the size of the correlations.\n\nJoint work with Lihan Wang and Quinn Winters.
LOCATION:Endenicher Allee 60
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