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DTSTART;TZID=Europe/Rome:20251003T110000
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DTSTAMP:20260428T203250
CREATED:20250925T093902Z
LAST-MODIFIED:20250925T093902Z
UID:26593-1759489200-1759496400@www.dica.polimi.it
SUMMARY:Solution of Inverse Problems of the Heat Equation using Shape Optimization and a Fast Parabolic Boundary Element Solver
DESCRIPTION:Venerdì 3 ottobre si terrà un seminario presso l’aula 087 (Edificio 4) alle ore 11:00 dal titolo “Solution of Inverse Problems of the Heat Equation using Shape Optimization and a Fast Parabolic Boundary Element Solver”. \nIl seminario sarà tenuto dal Prof. Johannes Tausch\, Southern Methodist University. \nAbstract \nA typical inverse problem is to determine the shape of an inclusion from measurements of temperatures and heat fluxes on the exterior boundary. This is known to be a severely ill posed problem. One way to improve the conditioning is to incorporate transient temperature information which leads to an inverse problem of the transient heat equation. \nOur approach is to minimize the difference of the boundary data obtained with a given shape and the measured data. In addition\, descent based optimization will be applied to find the optimal shape. To that end\, the concept of the shape gradient is introduced\, which describes the change of the solution of the heat equation with respect to changing the geometry of the domain. We will then show that the shape gradient can be computed by solving a state and an adjoint equation\, which are forward problems of the heat equation. \nThe latter problems are be solved using parabolic boundary integral equations. Here a fast method is used to efficiently evaluate the time convolutions of parabolic layer potentials. \nThe talk will conclude with numerical experiments that illustrate the efficiency and reconstruction quality of the approach. \n\nSpeaker’s bio\n\nJohannes Tausch received a PhD from Colorado State University and was a postdoctoral researcher at the Research Lab of Electronics at MIT. He is now a professor of mathematics at Southern Methodist University. His expertise includes numerical analysis and scientific computation\, with applications to wave propagation\, heat transfer and inverse problems. He is the managing editor of the Journal of Integral Equations and Applications.
URL:https://www.dica.polimi.it/it/evento/solution-of-inverse-problems-of-the-heat-equation-using-shape-optimization-and-a-fast-parabolic-boundary-element-solver/
CATEGORIES:Seminari e conferenze
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