On the use of multigrid preconditioners for topology optimization

Darin Peetz, Ahmed Elbanna

Research output: Contribution to journalArticlepeer-review


Topology optimization for large-scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the finite element analysis (FEA). However, the preconditioners used in these works vary, and in many cases are notably suboptimal. A handful of works have already demonstrated the effectiveness of geometric multigrid (GMG) preconditioners in topology optimization. We provide a direct comparison of GMG preconditioners with algebraic multigrid (AMG) preconditioners. We demonstrate that AMG preconditioners offer improved robustness over GMG preconditioners as topologies evolve, albeit with a higher overhead cost. In 2D the gain from increased robustness more than offsets the overhead cost. However, in 3D the overhead becomes prohibitively large. We thus demonstrate the benefits of mixing geometric and algebraic methods to limit overhead cost while improving robustness, particularly in 3D.

Original languageEnglish (US)
Pages (from-to)835-853
Number of pages19
JournalStructural and Multidisciplinary Optimization
Issue number2
StatePublished - Feb 2021


  • Multigrid
  • Topology optimization

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


Dive into the research topics of 'On the use of multigrid preconditioners for topology optimization'. Together they form a unique fingerprint.

Cite this