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Cyclic and feedback vertex set ordering for the 2d convection-diffusion equation
Iterative solvers like multigrid methods are very fast for elliptic problems like the Poisson or Stokes equations. However, in the presence of dominant convection as it might appear in models in computational fluid dynamics, the convergence rate typically decreases. Examples are the convection-diffusion equation or the Navier-Stokes equations. A robust method can be obtained by an appropriate ordering of the unknowns. We propose ordering algorithms that yield a numbering together with a block structure which can be used for a (block) iterative method as a smoother in the multigrid iteration or as a preconditioner in Krylov-methods. We illustrate the methods for some two dimensional test problems.
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