Numerical Model Reduction with error estimation for computational homogenization of non-linear consolidation

Journal article, 2022

Numerical Model Reduction (NMR) is adopted for solving the non-linear microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using Proper Orthogonal Decomposition and the pertinent displacement basis is obtained using Nonuniform Transformation Field Analysis. An explicit, fully computable, a posteriori error estimator is derived based on the linearized error equation for quantification of the NMR error in terms of a suitably chosen energy norm. The performance of the error estimates is demonstrated via a set of numerical examples with varying load amplitudes.