Monte-Carlo and sensitivity transport models for domain deformation. (August 2020) - Lapeyre, P.; Blanco, S.; Caliot, C.; Dauchet, J.; El Hafi, M.; Fournier, R.; Farges, O.; Gautrais, J.; Roger, M.
Highlights: Sensitivity transport models are presented in order to estimate the shape derivatives of objective functions in the context of radiative transfers. Regarding the sensitivity transport, the sources of geometrical sensitivities emerge as boundary conditions. Different types of sensitivity sources are identified and illustrated in four configurations involving semi-transparent medium, reflective surfaces and curved surfaces. The Monte Carlo method is used to solve the sensitivity model and we use two configurations to illustrate how we extend it to complex geometries ; we also show that it does not present any convergence issue. Abstract: We address the question of evaluating shape derivatives of objective functions for radiative-transfer engineering involving semi-transparent media. After recalling the standard Monte-Carlo approach to sensitivity estimation and its current limitations, a new method is presented for the specific case of geometrical sensitivities. This method is then tested on configurations with multiple-scattering and absorbing (non-emitting) semi-transparent medium. A new geometrical sensitivity algorithm is presented with full details in order to extend, on several examples, its implementation in complex geometries.