Monte-Carlo and Domain-Deformation Sensitivities

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 in a square cavity filled by a multiple-scattering and absorbing (non-emitting) semi-transparent medium, irradiated by an emissive cylinder. A new geometrical sensitivity algorithm is presented with full genericity in order to allow its future implementation in complex geometries.

Path integrals formulations leading to propagator evaluation for coupled linear physics in large geometric models

“…If only sensitivities were required, i.e. the derivative with respect to each parameter, then the general theory of sensitivity evaluation in Monte Carlo algorithms could be used [23], but we would not build the complete dependence (the function) as we did here with the sources. Addressing the complete non-linear dependence on other parameters than sources is not theoretically unfeasible: it has notably been achieved in the field of radiative transfer under the literature name of "Symbolic Monte Carlo" [24,25,26,27] and we have started to work on extending these symbolic techniques to coupled heat transfer, with the objective of implementing them inside stardis-solver [28,29].…”