From: bangerth Date: Mon, 11 Aug 2008 23:12:50 +0000 (+0000) Subject: Use only the allowed range h3...h6 instead of h2... X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3e126410edfa42f1b50e11474b0fe836168c13d4;p=dealii-svn.git Use only the allowed range h3...h6 instead of h2... git-svn-id: https://svn.dealii.org/trunk@16514 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-22/doc/results.dox b/deal.II/examples/step-22/doc/results.dox index 524f831902..acc4fe0b44 100644 --- a/deal.II/examples/step-22/doc/results.dox +++ b/deal.II/examples/step-22/doc/results.dox @@ -312,10 +312,10 @@ is not a good choice in 3D - a full decomposition needs many new entries that -

Possible Extensions

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Possible Extensions

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Improved linear solver in 3D

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Improved linear solver in 3D

We have seen in the section of computational results that the number of outer @@ -350,7 +350,7 @@ in the early tutorial programs. The improvements are still rather unsatisfactory, if one compares with an elliptic problem of similar size. -

Better ILU decomposition by smart reordering

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Better ILU decomposition by smart reordering
A first attempt to improve the speed of the linear solution process is to choose a dof reordering that makes the ILU being closer to a full LU decomposition, as @@ -370,13 +370,13 @@ case, the renumbering takes about 5 times as much memory, which yields an infeasible algorithm for the last cycle in 3D with 1.2 million unknowns. -

Better preconditioner for the inner CG solver

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Better preconditioner for the inner CG solver
Another idea to improve the situation even more would be to choose a preconditioner that makes CG for the (0,0) matrix $A$ converge in a mesh-independent number of iterations, say 10 to 30. We have seen such a canditate in @ref step_16 "step-16": multigrid. -

Block Schur complement preconditioner

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Block Schur complement preconditioner
But even with a good preconditioner for $A$ at hand, we still need to solve of the same linear system repeatedly (with different right hand sides, though). The approach we are going to discuss here is how this @@ -758,12 +758,12 @@ problem size than CG (as explained above). Nonetheless, the improvement by a factor of 3-5 for moderate problem sizes is quite impressive. -

Combining block preconditioner and multigrid

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Combining block preconditioner and multigrid
An ultimate linear solver for this problem could be imagined as a combination of an optimal preconditioner for $A$ (e.g. multigrid) and the block preconditioner described above. -

No block matrices and vectors

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No block matrices and vectors
Another possibility that can be taken into account is to not set up a block system, but rather solve the system of velocity and pressure all at once. The options are direct solve with UMFPACK (2D) or GMRES with ILU