In reservoir engineering, it is attractive to characterize the difference between reservoir models in metrics that relate to the economic performance of the reservoir as well as to the underlying geological structure. In this paper, we develop a dissimilarity measure that is based on reservoir flow patterns under a particular operational strategy. To this end, a spatial-temporal tensor representation of the reservoir flow patterns is used, while retaining the spatial structure of the flow variables. This allows reduced-order tensor representations of the dominating patterns and simple computation of a flow-induced dissimilarity measure between models. The developed tensor techniques are applied to cluster model realizations in an ensemble, based on similarity of flow characteristics.

The imaging quality of the projection optics of an extreme ultraviolet lithography scanner degrades under the influence of thermally induced deformations of its mirrors. Wavefronts of different reticle points encounter different parts of the deformed mirrors, resulting in a field dependent wavefront error. This paper presents how ideas from multi-conjugate adaptive optics can be used to reduce these thermally induced aberrations. To this end a generic deformable mirror model is implemented. Linear actuator sensitivities are derived directly, based on nominal ray locations and directions, enabling fast prototyping. An integrated opto-thermo-mechanical mirror heating model is used to determine the evolution of thermally induced abberations over time. This transient simulation is used to analyze four different adaptive optics configurations and two different control algorithms. It is shown that by employing the multi-objective goal-attainment method, it is possible to improve the optical performance significantly when compared to minimizing the ℓ₂-norm of the total residual wavefront error vector.