A separated representation involving multiple time scales within the Proper Generalized Decomposition framework

Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale accurately predict response system. In this paper, we provide an alternative route circumvent prohibitive meshes arising from necessity capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within standard Proper Generalized Decomposition, where coordinate transformed into multi-dimensional through new separated coordinates, each representing one scale, while continuity ensured in coupling. For instance, when considering two different scales, governing Partial Differential Equation commuted nonlinear system that iterates between so-called microtime and macrotime, so be viewed as 2D time. macroscale effects taken account by means finite element-based macro-discretization, whereas microscale handled with unidimensional parent spaces replicated throughout domain. resulting allows us very fine without impacting computational efficiency. formulation explored numerically verified thermal elastodynamic problems.