# Multigrid reduction preconditioning framework for coupled processes in porous and fractured media

arXiv: https://arxiv.org/abs/2101.11649 · HTML: https://mlsanity.com/paper/2101.11649/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2021.

## Built on by (most cited first, 5 of 5)

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- [Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Data](https://mlsanity.com/paper/2408.01575/) (2024)
- [Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations](https://mlsanity.com/paper/2408.10717/) (2024)
- [Prediction of Fault Slip Tendency in CO2 Storage using Data-space Inversion](https://mlsanity.com/paper/2601.05431/) (2026)
- [Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage](https://mlsanity.com/paper/2608.02629/) (2026)

## Abstract (arXiv)

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design efficient and safe operations, numerical simulations are widely used. Given the relatively long time-scales of interest, fully-implicit time-stepping schemes are often necessary to avoid time-step stability restrictions. A major computational bottleneck for these methods, however, is the linear solver. These systems are extremely large and ill-conditioned. Because of the wide range of processes and couplings that may be involved--e.g. formation and propagation of fractures, deformation of the solid porous medium, viscous flow of one or more fluids in the pores and fractures, complicated well sources and sinks, etc.--it is difficult to develop general-purpose but scalable linear solver frameworks. This challenge is further aggravated by the range of different discretization schemes that may be adopted, which have a direct impact on the linear system structure. To address this obstacle, we describe a flexible framework based on multigrid reduction that can produce purely algebraic preconditioners for a wide spectrum of relevant physics and discretizations. We demonstrate its broad applicability by constructing scalable preconditioners for several problems, notably: a hybrid discretization of single-phase flow, compositional multiphase flow with complex wells, and hydraulic fracturing simulations. Extension to other systems can be handled quite naturally. We demonstrate the efficiency and scalability of the resulting solvers through numerical examples of difficult, field-scale problems.