From e9465fc11158eab006b29ba884958f77fd25e85a Mon Sep 17 00:00:00 2001 From: kronbichler Date: Mon, 13 Oct 2008 13:21:29 +0000 Subject: [PATCH] Added a bit more information about the Stokes preconditioner. git-svn-id: https://svn.dealii.org/trunk@17191 0785d39b-7218-0410-832d-ea1e28bc413d --- .../lac/include/lac/trilinos_precondition_block.h | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/deal.II/lac/include/lac/trilinos_precondition_block.h b/deal.II/lac/include/lac/trilinos_precondition_block.h index 25aff1116f..ce54090a1f 100644 --- a/deal.II/lac/include/lac/trilinos_precondition_block.h +++ b/deal.II/lac/include/lac/trilinos_precondition_block.h @@ -90,16 +90,26 @@ namespace TrilinosWrappers // Forward declarations. -/** +/** * This class implements a black box preconditioner for saddle points * systems arising from the Stokes or Navier–Stokes equations as * specified by the papers D. Silvester, A. Wathen, Fast iterative * solution of stabilised Stokes systems part II. Using general block - * preconditioners, SIAM J. Numer. Anal. 31:1352&ndash1367 (1994) + * preconditioners, SIAM J. Numer. Anal. 31:1352–1367 (1994) * and D. Kay, D. Loghin, A. Wathen, A preconditioner for the * steady-state Navier–Stokes equations, SIAM * J. Sci. Comput. 24(1):237–256 (2002), respectively. * + * The preconditioner is based an approximation to the Schur + * complement of the block matrix. The Schur complement $S=B + * A_{\mathbf u}^{-1} B^T$ is approximated by a mass matrix $M_p$ on + * the pressure space in the case of the Stokes equations, and as a + * product $S^{-1} = L_p^{-1} F_p M_p^{-1}$ with pressure Laplace + * matrix $L_p$, pressure convection-diffusion operator $F_p$ + * (corresponding to the sum of time derivative, convection and + * diffusion), and pressure mass matrix $M_p$ in the case of the + * Navier–Stokes equations. + * * @ingroup TrilinosWrappers * @ingroup Preconditioners * @author Martin Kronbichler, 2008 -- 2.39.5