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.

数值模型约简 (NMR) 用于解决以位移和压力为未知场的多孔介质模型问题的计算均质化所产生的非线性微尺度问题。使用适当正交分解获得压力场的简化基础，使用非均匀变换场分析获得相关位移基础。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. 误差估计的性能通过一组具有变化负载幅度的数值例子来证明。