On the Spectral Clustering in Algebraic Multigrid Methods

2025/11/15 by José Pablo Lucero Lorca, Lorca, Jose Pablo Lucero, McCoid, Conor +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2511.12298

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

We introduce a new direct multilevel method for solving arbitrary complex square linear systems that uses a regular smoother and an arbitrary but equal number of pre- and post-smoothings. Through careful analysis of the error propagation operator, we cluster the spectrum of this operator. This allows us to write a direct K-cycle version of the method.

Citations

• Towards a Multigrid Preconditioner Interpretation of Hierarchical Poincaré-Steklov Solvers
• Towards modular Hierarchical Poincaré-Steklov solvers
• On an efficient line smoother for the p-multigrid γ-cycle
• Should multilevel methods for discontinuous Galerkin discretizations use discontinuous interpolation operators?
• Optimization of two-level methods for DG discretizations of reaction-diffusion equations
• On the Ideal Interpolation Operator in Algebraic Multigrid Methods
• The Hierarchical Poincare-Steklov (HPS) solver for elliptic PDEs: A tutorial

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