Bootstrap Algebraic Multigrid: status report, open problems, and outlook

TL;DR

This paper reviews the bootstrap algebraic multigrid (BAMG) methodology, discussing key ideas, recent research developments, open problems, and presenting results on diffusion problems with oscillatory coefficients.

Contribution

It provides a comprehensive overview of BAMG, including new insights into its components and applications, and highlights open problems for future research.

Findings

Effective coarsening strategies using algebraic distances

Accurate prolongation operators computed via least squares

Successful application to diffusion problems with oscillatory coefficients

Abstract

This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm.