Corno, Jacopo (2017)
Numerical Methods for the Estimation of the Impact of Geometric Uncertainties on the Performance of Electromagnetic Devices.
Technische Universität Darmstadt
Dissertation, Erstveröffentlichung

Kurzbeschreibung (Abstract)

This work addresses the application of Isogeometric Analysis to the simulation of particle accelerator cavities and other electromagnetic devices whose performance is mainly determined by their geometry. By exploiting the properties of B-Spline and Non-Uniform B-Spline basis functions, the Isogeometric approximation allows for the correct discretisation of the spaces arising from Maxwell's equations and for the exact representation of the computational domain. This choice leads to substantial improvements in both the overall accuracy and computational effort.

The suggested framework is applied to the evaluation of the sensitivity of these devices with respect to geometrical changes using Uncertainty Quantification methods and to shape optimisation processes. The particular choice of basis functions simplifies the construction of the geometry deformations significantly.

Finally, substructuring methods are proposed to further reduce the computational cost due to matrix assembly and to allow for hybrid coupling of Isogeometric Analysis and more classical Finite Element Methods. Considerations regarding the stability of such methods are addressed.

The methods are illustrated by simple numerical tests and real world device simulations with particular emphasis on particle accelerator cavities.

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