Accounting for weak discontinuities and moving boundaries in the context of the Natural Element Method and model reduction techniques

Several thermomechanical models are defined in evolving domains involving fixed and evolving discontinuities. The accurate representation of moving boundaries and interfaces is, despite the significant progresses achieved in the recent years, an active research domain. This work focusses on the application of meshless methods for discretizing this kind of models, and in particular the ones based on the use of natural neighbor interpolations. The questions related to the description of moving boundaries, evolving weak discontinuities and the possibility of an eventual model reduction to alleviate the computational simulation cost, will be some of the topics here analyzed.