Applied Mathematics, Computation and Simulation: Part IV

Chairman

Talk 1

Title:
Robust mission design using invariant manifolds. Application to asteroid exploration.

Speaker:
Lamberto Dell’Elce (Post Doc) – McTAO

Abstract:
When a deterministic system is considered, any initial condition on an invariant manifold generates a trajectory that entirely lies on the manifold itself. However, owing to modeling assumptions and uncertainties in the dynamical environment, the evolution of trajectories on the manifold will generally drift from the nominal path in a real-life scenario. In this talk, invariant manifolds are exploited to tackle mission design in the presence of possibly-non-Gaussian uncertainties in the dynamical environment. In a Lyapunov stability perspective, our objective is to find a volume of the phase space such that the flow emanated from this set is guaranteed to evolve in a prescribed bounded region for all possible realizations of the uncertain quantities. This concept is formulated as a semi-infinite optimization problem aimed at maximizing the volume of the feasible region. The methodology is illustrated in the framework of space missions to small bodies, which are characterized by a strongly perturbed dynamical environment.

Talk 2

Title:
Numerical strategies for discontinuous Galerkin time domain methods in the context of nanophotonics and radar applications

Speaker:
Nikolai Schmitt and Alexis Gobe – Nachos

Abstract:
We present recent advances of the development on Discontinuous Galerkin Time Domain (DGTD) solvers for computational nanophotonics, focusing on metallic nanostructures irradiated by laser pulses. In particular, we deal with the numerical modeling of a nonlocal dispersion model which is coupled to 3D Maxwell’s equations in time domain. The second part of our contribution addresses advanced meshing techniques for nanophotonics and radar applications. A reasonable number of realistic simulation setups consist of a dominating vacuum fraction around the objects of interest. However, these geometrically complex objects require a high spatial mesh resolution compared to free space propagation. We exploit the local formulation of DGTD methods in order to use hybrid meshes that contain tetrahedral and hexahedral elements in order to reduce the over all amount of degrees of freedom.

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