Coarse-grid selection using simulated annealing

Tareq Uz Zaman, Scott P. MacLachlan, Luke N. Olson, Matthew West

Research output: Contribution to journalArticlepeer-review


Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying problem and its discretization, algebraic multigrid aims to be less intrusive, requiring less knowledge about the origin of the linear system. A key step in algebraic multigrid is the choice of the coarse/fine partitioning, aiming to balance the convergence of the iteration with its cost. In work by MacLachlan and Saad (2007), a constrained combinatorial optimization problem is used to define the “best” coarse grid within the setting of a two-level reduction-based algebraic multigrid method and is shown to be NP-complete. Here, we develop a new coarsening algorithm based on simulated annealing to approximate solutions to this problem, which yields improved results over the greedy algorithm developed previously. We present numerical results for test problems on both structured and unstructured meshes, demonstrating the ability to exploit knowledge about the underlying grid structure if it is available.

Original languageEnglish (US)
Article number115263
JournalJournal of Computational and Applied Mathematics
StatePublished - Oct 15 2023
Externally publishedYes


  • Algebraic multigrid
  • Coarse-grid selection
  • Combinatorial optimization
  • Simulated annealing

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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