On geometric aspects of Algebraic Multigrid methods

• Date: 15. 10. 2026
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: José Pablo Lucero Lorca

Domain decomposition and multigrid methods are closely related, although their development has traditionally emphasized different perspectives. While domain decomposition methods are naturally motivated by geometric partitions and local problems, algebraic multigrid methods describe the same underlying structures through operators and matrix factorizations. In this talk, we explore these connections through the geometric interpretation of recent results on direct algebraic multigrid methods. We examine how subdomain corrections, Schur complements, and coarse spaces arise naturally from hierarchical elimination, and how these ingredients relate to classical Schwarz methods. We then discuss how suitable choices of smoothing and coarse correction lead to remarkable spectral clustering properties, providing a connection between geometric constructions and direct solution methods for general linear systems.