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

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. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This paper adopts Numerical Model Reduction (NMR) to solve the nonlinear microscale problem in computational homogenization of porous media. It derives an explicit and computable a posteriori error estimator based on the linearized error equation and demonstrates its performance through numerical examples.