From 1bde34bb6b22bde849d6b9a15b0a2bcb68b697fa Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Thu, 28 Apr 2011 13:33:23 +0000 Subject: [PATCH] Add a note taken pretty much verbatim from an email by Joshua White. git-svn-id: https://svn.dealii.org/trunk@23662 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-46/doc/results.dox | 31 +++++++++++++++++++----- 1 file changed, 25 insertions(+), 6 deletions(-) diff --git a/deal.II/examples/step-46/doc/results.dox b/deal.II/examples/step-46/doc/results.dox index 86cfc1634c..e96291f8c8 100644 --- a/deal.II/examples/step-46/doc/results.dox +++ b/deal.II/examples/step-46/doc/results.dox @@ -239,12 +239,31 @@ One can therefore expect that @f] would be a good preconditioner if $\widetilde{A_{\text{fluid}}^{-1}} \approx A_{\text{fluid}}^{-1}, \widetilde{A_{\text{solid}}^{-1}} -\approx A_{\text{solid}}^{-1}$. That means, we only need good -preconditioners for Stokes and the elasticity equations -separately. These are well known, however: for Stokes, we can use the -preconditioner discussed in the results section of step-22; for -elasticity, a good preconditioner would be a single V-cycle of a -geometric or algebraic multigrid. +\approx A_{\text{solid}}^{-1}$. + +That means, we only need good preconditioners for Stokes and the +elasticity equations separately. These are well known, however: for +Stokes, we can use the preconditioner discussed in the results section +of step-22; for elasticity, a good preconditioner would be a single +V-cycle of a geometric or algebraic multigrid. There are more open +questions, however: For an "optimized" solver block-triangular +preconditioner built from two sub-preconditioners, one point that +often comes up is that, when choosing parameters for the +sub-preconditioners, values that work well when solving the two +problems separately may not be optimal when combined into a +multiphysics preconditioner. In particular, when solving just a solid +or fluid mechanics problem separately, the balancing act between the +number of iterations to convergence and the cost of applying the +preconditioner on a per iteration basis may lead one to choose an +expensive preconditioner for the Stokes problem and a cheap +preconditioner for the elasticity problem (or vice versa). When +combined, however, there is the additional constraint that you want +the two sub-preconditioners to converge at roughly the same rate, or +else the cheap one may drive up the global number of iterations while +the expensive one drives up the cost-per-iteration. For example, while a single AMG +V-cycle is a good approach for elasticity by itself, when combined +into a multiphysics problem there may be an incentive to using a full +W-cycle or multiple cycles to help drive down the total solve time.

Refinement indicators

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