From 5bb875298a64a2a354237d91bf89c728b1eef80b Mon Sep 17 00:00:00 2001 From: Guido Kanschat Date: Fri, 23 Mar 2001 16:27:27 +0000 Subject: [PATCH] Documentation fixed git-svn-id: https://svn.dealii.org/trunk@4279 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/lac/include/lac/schur_matrix.h | 23 ++++++++++++----------- 1 file changed, 12 insertions(+), 11 deletions(-) diff --git a/deal.II/lac/include/lac/schur_matrix.h b/deal.II/lac/include/lac/schur_matrix.h index dbd2140161..45deeca3a6 100644 --- a/deal.II/lac/include/lac/schur_matrix.h +++ b/deal.II/lac/include/lac/schur_matrix.h @@ -27,20 +27,20 @@ template class BlockVector; * * Given a non-singular matrix @p{A} (often positive definite) and a * positive semi-definite matrix @p{C} as well as matrices @p{B} and - * @{Dt} of full rank, this class implements a new matrix, the Schur + * @p{Dt} of full rank, this class implements a new matrix, the Schur * complement a the system of equations of the structure * - * \begin{verbatim} + * @begin{verbatim} * / \ / \ / \ * | A Dt | | u | - | f | * | -B C | | p | - | g | * \ / \ / \ / - * \end{verbatim} + * @end{verbatim} * * Multiplication with the Schur matrix @p{S} is the operation - * \begin{verbatim} + * @begin{verbatim} * S p = C p + B A-inverse Dt-transpose p, - * \end{verbatim} + * @end{verbatim} * which is an operation within the space for @p{p}. * * The data handed to the Schur matrix are as follows: @@ -58,27 +58,28 @@ template class BlockVector; * * All matrices involved are of arbitrary type and vectors are * @ref{BlockVector}s. This way, @p{SchurMatrix} can be coupled with - * any matrix classes providing @p{vmult} and @p{Tvmult} and even - * nested. + * any matrix classes providing @p{vmult} and @p{Tvmult} and can be + * even nested. Since @ref{SmartPointer}s of matrices are stored, the + * matrix blocks should be derived from @ref{Subscriptor}. * * Since the Schur complement of a matrix corresponds to a Gaussian * block elimination, the right hand side of the condensed system must * be preprocessed. Furthermore, the eliminated variable must be * reconstructed after solving. * - * \begin{verbatim} + * @begin{verbatim} * g = g + B A-inverse f * u = A-inverse (f - D-transpose p) - * \end{verbatim} + * @end{verbatim} * * Applying these transformations, the solution of the system above by a * @p{SchurMatrix} @p{schur} is coded as follows: * - * \begin{verbatim} + * @begin{verbatim} * schur.prepare_rhs (g, f); * solver.solve (schur, p, g, precondition); * schur.postprocess (u, p); - * \end{verbatim} + * @end{verbatim} * * @author Guido Kanschat, 2000, 2001 */ -- 2.39.5