Efficient uncertainty propagation for photonics: Combining Implicit Semi-analog Monte Carlo (ISMC) and Monte Carlo generalised Polynomial Chaos (MC-gPC)

In this paper, we build wellposed intrusive generalised Polynomial Chaos (gPC) based reduced models for uncertain photonics. We solve the with a Monte-Carlo (MC) scheme. Care is taken to highlight under which condition model (gPC or not) wellposed. The analysis carried out thanks an analogy between construction of uncertainty quantification and kinetic equations. order enforce aforementioned wellposedness conditions, several strategies, inspired from hyperbolicity-preserving ones [1], [2], [3], [4], [5], [6], [7], [8] are reviewed, adapted analysed. resolution performed astute combination Implicit Semi-analog MC (ISMC, see [9]) scheme photonics MC-gPC (see [10]) propagation. This work demonstrates that can be efficiently applied stiff nonlinear set partial derivative equations if allows fast convergence respect both time spatial discretisations (the latter properties being allowed by ISMC). Several benchmarks investigated in last section, they allow illustrating important aspects new ISMC-gPC solver