Convergent adaptive iterative schemes for solving multi-physics problems

TL;DR

This paper introduces a flexible framework for developing adaptive iterative algorithms to efficiently solve complex multi-physics problems, utilizing extit{a posteriori} estimators for method success prediction and adaptive control.

Contribution

It presents a general approach for creating adaptive iterative schemes with extit{a posteriori} estimators, enabling adaptive switching, time-stepping, and parameter tuning for multi-physics problems.

Findings

Effective adaptive algorithms for multi-physics problems

Successful application to porous media flow and poroelasticity

Improved convergence and efficiency demonstrated

Abstract

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori} estimators to predict the success or failure of the method. Based on these estimators, we propose adaptive algorithms, including adaptively switching between methods, adaptive time-stepping methods, and the adaptive tuning of stabilization parameters. We apply this framework to two-phase flow in porous media, surfactant transport in porous media, and quasi-static poroelasticity.