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*                          Einladung
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*                     Informatik-Oberseminar
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Zeit:  Montag, 9. Mai 2022, 15:00 Uhr
Zoom:
https://rwth.zoom.us/j/98637141061?pwd=Qkw3blFhWEIrelduWmpPSGNtQnN4dz09

Meeting ID: 986 3714 1061
Passcode: 618965

Referent: Jonathan Hüser, M.Sc.
          Lehrstuhl Informatik 12

Thema: Discrete Tangent and Adjoint Sensitivity Analysis for Discontinuous
       Solutions of Hyperbolic Conservation Laws

Abstract:

We consider the discrete tangent and adjoint sensitivities computed via
algorithmic differentiation of shock capturing numerical methods for
hyperbolic conservation laws which are widely used for models of fluid
dynamics such as those based on the Euler equations.
For discontinuous solutions the discrete sensitivities do not generally
converge to the correct sensitivities of the analytical solution as the
discretization grid is refined because the analytical sensitivities are
singular at the discontinuities of the solution.

In this thesis we propose a convergent numerical approximation of the
correct sensitivities of shock discontinuities in discontinuous solutions
of hyperbolic conservations laws with respect to the parameters of the
initial data.
We compute the shock sensitivities by approximating the Rankine-Hugoniot
condition taking into consideration the numerical viscosity of shock
capturing numerical methods in a way that can be computed by algorithmic
differentiation tools.
The resulting discrete sensitivities enable for example the gradient-based
parameter optimization of optimization problems constrained by a hyperbolic
conservation law.


Es laden ein: die Dozentinnen und Dozenten der Informatik