]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Added a bit more information about the Stokes preconditioner.
authorkronbichler <kronbichler@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 13 Oct 2008 13:21:29 +0000 (13:21 +0000)
committerkronbichler <kronbichler@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 13 Oct 2008 13:21:29 +0000 (13:21 +0000)
git-svn-id: https://svn.dealii.org/trunk@17191 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/lac/include/lac/trilinos_precondition_block.h

index 25aff1116fa0a121ad7942a5667da9c1672977ab..ce54090a1f41d1939cacf9094d189859385fab02 100644 (file)
@@ -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&ndash;Stokes equations as
  * specified by the papers <em>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)</em>
+ * preconditioners, SIAM J. Numer. Anal. 31:1352&ndash;1367 (1994)</em>
  * and <em> D. Kay, D. Loghin, A. Wathen, A preconditioner for the
  * steady-state Navier&ndash;Stokes equations, SIAM
  * J. Sci. Comput. 24(1):237&ndash;256 (2002)</em>, 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&ndash;Stokes equations.
+ *
  * @ingroup TrilinosWrappers
  * @ingroup Preconditioners
  * @author Martin Kronbichler, 2008

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