From: Timo Heister <timo.heister@gmail.com>
Date: Thu, 27 Feb 2020 20:17:04 +0000 (-0500)
Subject: amend FGMRES documentation
X-Git-Tag: v9.2.0-rc1~489^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=fc9f6b7c7c97bd584252e0ddcff8f2c9515c3da7;p=dealii.git

amend FGMRES documentation
---

diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib
index 8817762b27..b3ea97f3d6 100644
--- a/doc/doxygen/references.bib
+++ b/doc/doxygen/references.bib
@@ -483,3 +483,13 @@ MRREVIEWER = {Jose Luis Gracia},
   pages={3596--3604},
   year={2018}
 }
+
+@TechReport{Saad1991,
+  Title                    = {{A {F}lexible {I}nner-{O}uter {P}reconditioned {GMRES} {A}lgorithm}},
+  Author                   = {Y. Saad},
+  Institution              = {Minnesota Supercomputer Institute},
+  Year                     = {1991},
+  Address                  = {University of Minnesota},
+  Number                   = {91-279},
+  Url                      = {citeseer.ist.psu.edu/saad93flexible.html}
+}
diff --git a/include/deal.II/lac/solver_gmres.h b/include/deal.II/lac/solver_gmres.h
index 09eec56065..42c4f6f2a7 100644
--- a/include/deal.II/lac/solver_gmres.h
+++ b/include/deal.II/lac/solver_gmres.h
@@ -440,19 +440,23 @@ protected:
 
 /**
  * Implementation of the Generalized minimal residual method with flexible
- * preconditioning method.
+ * preconditioning (flexible GMRES or FGMRES).
  *
- * This version of the GMRES method allows for the use of a different
+ * This flexible version of the GMRES method allows for the use of a different
  * preconditioner in each iteration step. Therefore, it is also more robust
  * with respect to inaccurate evaluation of the preconditioner. An important
- * application is also the use of a Krylov space method inside the
+ * application is the use of a Krylov space method inside the
  * preconditioner. As opposed to SolverGMRES which allows one to choose
  * between left and right preconditioning, this solver always applies the
  * preconditioner from the right.
  *
  * FGMRES needs two vectors in each iteration steps yielding a total of
  * <tt>2*SolverFGMRES::AdditionalData::max_basis_size+1</tt> auxiliary
- * vectors.
+ * vectors. Otherwise, FGMRES requires roughly the same number of operations
+ * per iteration compared to GMRES, except one application of the
+ * preconditioner less at each restart and at the end of solve().
+ *
+ * For more details see @cite Saad1991.
  *
  * @author Guido Kanschat, 2003
  */