A Monolithic Algebraic Multigrid Framework for Multiphysics Applications with Examples from Resistive MHD

TL;DR

This paper introduces a flexible, monolithic algebraic multigrid framework designed for multiphysics problems, demonstrated through applications to resistive magnetohydrodynamics, enabling tailored and efficient solutions for complex coupled systems.

Contribution

The paper presents a novel monolithic multigrid framework that constructs and adapts multigrid components for multiphysics linear systems in a blocked, customizable manner.

Findings

Effective for resistive MHD sub-problems

Allows tailored multigrid component development

Demonstrates potential for complex multiphysics applications

Abstract

A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear systems coming from discretized partial differential equations. The main idea centers on developing multigrid components in a blocked fashion where each block corresponds to separate sets of physical unknowns and equations within the larger discretization matrix. Once defined, these components are ultimately assembled into a monolithic multigrid solver for the entire system. We demonstrate the potential of the framework by applying it to representative linear solution sub-problems arising from resistive MHD.