Methods toward better Multigrid Solver Convergence

TL;DR

This paper explores various factors affecting the convergence of multigrid solvers, including problem setup and solver parameters, through empirical studies on a Poisson problem to improve solver performance.

Contribution

It provides an experimental analysis of how different environmental and problem-specific conditions influence multigrid solver convergence, offering insights for better solver design.

Findings

Convergence varies with anisotropies and grid levels.

Preconditioner choice impacts solver efficiency.

Start vector and smoothing steps affect performance.

Abstract

I present a motivation of several areas where the Multigrid techniques can be employed. I present typical areas where the multigrid solver might be employed. I give an introduction to smoothers and how one might choose a preconditionor as well as an introduction of the Multigrid technique used. Then I do a study of the Multigrid technique while adjusting the environment conditions of the solver and the problem such as anisotropies, the grid-levels used, the preconditionor smoothing steps, the coordinate system and the start vector. The problem solved here was a simple Poisson problem. The Multigrid program used an F-cycle in this paper. I include performance study sections displaying results of the solver behavior under the different conditions.