Non-incremental strategies for simulating thermomechanical models with uncertainty

Description of complex materials involves numerous computational challenges. Thus, the analysis of transient models needs for intensive computation. In some of our former works we proposed a technique based on the separated representation of the unknown field able to circumvent the curse of dimensionality in the treatment of highly multidimensional models. In this work, we are addressing the challenge related to the transient behaviour. For this purpose we propose a separated representation of transient models leading to a non-incremental strategy, allowing to impressive CPU time savings. The use of separated representations allows computing the solution of transient parametric models (the parameters are assumed as additional coordinates). The parameters include thermal coefficients but also thermal sources and/or initial conditions. The resulting curse of dimensionality is circumvented by using the separated representation that implies a complexity that scales linearly with the dimension of the space.