Abstract
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.
Highlights
The complexity of coupled thermomechanical models defined in domains involving very fine space and time meshes induce computational issues
The use of explicit incremental methods is restricted to very short time steps because of the stability requirements
Implicit incremental methods need the solution of a linear system at each time step in the general non-linear case
Summary
The complexity of coupled thermomechanical models defined in domains involving very fine space and time meshes induce computational issues. Some times the parametric nature of such models (because of different uncertainties) induces additional difficulties. The use of explicit incremental methods is restricted to very short time steps because of the stability requirements. Implicit incremental methods need the solution of a linear system at each time step in the general non-linear case. The treatment of parametric models requires the solutions of many direct models. To circumvent these difficulties one could use reduced approximation bases within the incremental framework. Another possibility lies in the use of an alternative non-incremental technique. This work explores the use of a particular non-incremental technique based on the separated representation of the unknown field
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