Fast Online Adaptive Enrichment for Poroelasticity with High Contrast

TL;DR

This paper introduces an online adaptive enrichment technique within the CEM-GMsFEM framework to efficiently solve high-contrast linear heterogeneous poroelasticity models, improving accuracy through residual-driven basis functions.

Contribution

It presents a novel online adaptive enrichment method for poroelasticity models that adaptively constructs basis functions based on residuals, with theoretical analysis and numerical validation.

Findings

Enhanced accuracy in poroelasticity simulations with high contrast coefficients.

Effective reduction of error through residual-driven online basis functions.

Theoretical justification of the online enrichment algorithm.

Abstract

In this work, we develop an online adaptive enrichment method within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving the linear heterogeneous poroelasticity models with coefficients of high contrast. The proposed method makes use of information of residual-driven error indicators to enrich the multiscale spaces for both the displacement and the pressure variables in the model. Additional online basis functions are constructed in oversampled regions accordingly and are adaptively chosen to reduce the error the most. A complete theoretical analysis of the online enrichment algorithm is provided and justified by thorough numerical experiments.