POD-based reduced order modeling of global-in-time iterative decoupled algorithms for Biot's consolidation model

TL;DR

This paper develops a POD-based reduced order model for global-in-time iterative algorithms solving Biot's consolidation model, significantly reducing computational costs while maintaining accuracy.

Contribution

It introduces a novel reduced order modeling approach for global-in-time iterative algorithms applied to Biot's consolidation, enhancing efficiency.

Findings

The reduced order model effectively accelerates computations.

Numerical experiments confirm the accuracy and efficiency of the approach.

Theoretical analysis supports the convergence and stability of the method.

Abstract

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate the backward differentiation formulas for time discretization. In each iteration, these algorithms involve solving a diffusion subproblem over the entire temporal domain, followed by solving a generalized Stokes subproblem over the same time interval. To accelerate the global-in-time iterative process, we present a reduced order modeling approach based on proper orthogonal decomposition, aimed at reducing the primary computational cost from the generalized Stokes subproblem. The effectiveness of this novel method is validated both theoretically and through numerical experiments.