A Note on Algebraic Multigrid Methods for the Discrete Weighted Laplacian

TL;DR

This paper explores the adaptation of algebraic multigrid methods to solve large linear systems from weighted Laplacian problems, demonstrating their effectiveness through extensive numerical experiments.

Contribution

It introduces a tailored multigrid approach for weighted Laplacian systems and provides a critical analysis supported by comprehensive numerical testing.

Findings

Multigrid methods effectively solve weighted Laplacian systems.

Numerical experiments show promising convergence properties.

The approach adapts well to various boundary conditions.

Abstract

In recent contributions, algebraic multigrid methods have been designed and studied from the viewpoint of the spectral complementarity. In this note we focus our efforts on specific applications and, more precisely, on large linear systems arising from the approximation of weighted Laplacian with various boundary conditions. We adapt the multigrid idea to this specific setting and we present and critically discuss a wide numerical experimentation showing the potentiality of the considered approach.