From 5e5f1403c0af70137283935dc05013ba57d7c0a6 Mon Sep 17 00:00:00 2001
From: Matthias Maier <tamiko@43-1.org>
Date: Tue, 3 May 2022 16:08:02 -0500
Subject: [PATCH] Step-81: add two references

---
 doc/doxygen/references.bib       | 20 ++++++++++++++++++++
 examples/step-81/doc/results.dox |  6 ++++--
 2 files changed, 24 insertions(+), 2 deletions(-)

diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib
index d042c7b984..3a6663f6ba 100644
--- a/doc/doxygen/references.bib
+++ b/doc/doxygen/references.bib
@@ -1341,6 +1341,16 @@
   SERIES={International Series in Pure and Applied Physics},
 }
 
+@ARTICLE{Gopalakrishnan2003,
+  AUTHOR={J. Gopalakrishnan and Pasciak, J. E.},
+  TITLE={Overlapping Schwarz preconditioners for indefinite time harmonic
+    {M}axwell equations},
+  JOURNAL={Math. Comput.},
+  VOLUME={72},
+  PAGES={1-15},
+  YEAR={2003}
+}
+
 @BOOK{Monk2003,
   AUTHOR={P. Monk},
   TITLE={Finite Element Methods for {Maxwell's} Equations},
@@ -1367,6 +1377,16 @@
     year = {2017}
 }
 
+@ARTICLE{Ying2012,
+  TITLE={A sweeping preconditioner for time-harmonic {M}axwell's equations},
+  AUTHOR={P. Tsuji and B. Engquist and L. Ying},
+  YEAR={2012},
+  JOURNAL={J. Comput. Phys.},
+  VOLUME={231},
+  PAGES={3770-3783},
+}
+
+
 % ------------------------------------
 % Step 82
 % ------------------------------------
diff --git a/examples/step-81/doc/results.dox b/examples/step-81/doc/results.dox
index e62a77537b..0708833ed6 100644
--- a/examples/step-81/doc/results.dox
+++ b/examples/step-81/doc/results.dox
@@ -283,8 +283,10 @@ The example step could be extended in a number of different directions.
     Unfortunately, time-harmonic Maxwell's equations lack the usual notion
     of local smoothing properties, which renders the usual suspects, such
     as a geometric multigrid (see the Multigrid class), largely useless. A
-    possible extension would be to implement a Schwarz preconditioner
-    (based on domain decomposition), or a sweeping preconditioner.
+    possible extension would be to implement an additive Schwarz preconditioner
+    (based on domain decomposition, see for example
+    @cite Gopalakrishnan2003), or a sweeping preconditioner (see for
+    example @cite Ying2012).
   </li>
   <li>
     Another possible extension of the current program is to introduce local
-- 
2.39.5