Multigrid Solver with Line Smoothing

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Multigrid Solver with Line Smoothing
K. Fidkowski Advisor D. Darmofal
Line Smoother Motivation Strongly convective
systems characterized by transport of information
along characteristic directions
Lines in flow over a bump

• Procedure
• Construct lines of elements based on flow
  direction
• At each smoothing iteration, solve implicitly on
  the lines
• Use in conjunction with P-multigrid

• Full Multigrid (FMG)

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Results for Ringleb Flow
K. Fidkowski Advisor D. Darmofal
FMG with full convergence on each level
Ringleb accuracy vs. CPU time
Residual is converged to machine zero on each
level (p). Step-like error convergence indicative
of effective multigrid scheme.
Benefit of higher order evident by comparing p2
to p1 at a given accuracy level. Improvement in
CPU time is approx. two orders of magnitude
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