]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Add a paragraph about complex-valued problems.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Thu, 17 Mar 2005 14:40:30 +0000 (14:40 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Thu, 17 Mar 2005 14:40:30 +0000 (14:40 +0000)
git-svn-id: https://svn.dealii.org/trunk@10182 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/doc/faq.html

index 4b409d7e5ffc65a6fdf5868af7dc7fea38ff4daf..f9d7902b6c8431f892d4d4583dbe0a8299ab9952 100644 (file)
@@ -43,6 +43,7 @@
        <acronym>deal.II</acronym>?</a>
   <li> <a href="#problem-howto">How do I solve problem XXX with
        <acronym>deal.II</acronym>?</a>
+  <li> <a href="#problem-complex">Can I solve problems over complex numbers?</a>
   <li> <a href="#time-dependent">There is no tutorial program for
        time-dependent problems!</a>
   <li> <a href="#contribute">I want to contribute to the development
   </p>
 
 
+  <a name="problem-complex"></a>
+  <h3>Can I solve problems over complex numbers?</h3>
+
+  <p>
+  Yes, you can, and it has been done numerous times with
+  <acronym>deal.II</acronym>. However, we have a standard
+  recommendation: consider such problems as systems of partial
+  differential equations, where the individual components of the
+  solution are the real and imaginary part of your unknown. The reason
+  for this is that for complex-valued problems, the product
+  <tt>&lt;u,v&gt;</tt> of two vectors is not the same as
+  <tt>&lt;v,u&gt;</tt>, and it is very easy to get this wrong in many
+  places. If you want to avoid these common traps, then the easiest
+  way around is to split up you equation into two equations of real
+  and imaginary part first, and then treat the resulting system as a
+  system of real variables. This also makes the type of linear system
+  clearer that you get after discretization, and tells you something
+  about which solver may be adequate for it.
+  </p>
+
+
   <a name="time-dependent"></a>
   <h3>There is no tutorial program for
        time-dependent problems!</h3>

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