The ultraweak time coupling in non-linear multiphysics modelling and related optimization problems

This paper presents different strategies in order to solve forward direct and backward adjoint problems when dealing with coupled time-dependent electromagnetic and heat transfer phenomena, as well as related optimization problems. It is shown that the use of the fully discretized gradient method is judicious since the obtained gradient is exact while any other method yield to approximations of the gradient. The use of the ultraweak coupling and of the discretized gradient have been validated through different tests dealing with direct modelling, parameter identification and optimization