Looking for a Reference on Smoothers for FEA

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SUMMARY

The discussion focuses on the need for quantitative references regarding geometric multigrid (GMG) and Vanka smoothers in finite element analysis (FEA). Participants highlight the lack of detailed resources quantifying the cost reduction achieved by GMG smoothers. Additionally, the Vanka smoother is noted for its specialization in solving incompressible Navier-Stokes equations and its utility in managing zeros on the diagonals of sparse matrices. The request for comprehensive sources indicates a gap in available literature on these specific smoothing techniques.

PREREQUISITES
  • Understanding of finite element analysis (FEA)
  • Familiarity with multigrid methods
  • Knowledge of incompressible Navier-Stokes equations
  • Experience with sparse matrix operations
NEXT STEPS
  • Research quantitative studies on geometric multigrid (GMG) smoothers
  • Explore the Vanka smoother's application in incompressible Navier-Stokes problems
  • Investigate the impact of smoothers on the convergence rates in FEA
  • Review literature on sparse matrix techniques and their optimization
USEFUL FOR

Researchers, engineers, and practitioners in computational fluid dynamics, particularly those focused on finite element methods and multigrid techniques.

Twigg
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Hi all,

Can anyone point me to a quantitative explanation of the geometric multigrid and Vanka smoothers? I found a qualitative article describing the GMG smoother, but it doesn't quantify how much it reduces the cost of a problem. I have found nothing yet on the Vanka smoother except that it is specialized for the incompressible Navier-Stokes equations and that it might be used for handling zeros on the diagonals of a sparse matrix. Any sources or summaries you have are much appreciated!
 

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