<a href="../../doxygen/deal.II/step_33.html" target="body">33</a>
<a href="../../doxygen/deal.II/step_34.html" target="body">34</a>
<a href="../../doxygen/deal.II/step_35.html" target="body">35</a><br />
- <a href="../../doxygen/deal.II/step_36.html" target="body">36</a>
+ <a href="../../doxygen/deal.II/step_36.html" target="body">36</a>
+ <a href="../../doxygen/deal.II/step_37.html" target="body">37</a>
</p>
<hr>
<tr valign="top">
<td><a href="../../doxygen/deal.II/step_35.html">Step-35</a></td>
- <td> A projection solver for the Navier-Stokes equations.
+ <td> A projection solver for the Navier–Stokes equations.
</td></tr>
<tr valign="top">
<td> Using SLEPc for linear algebra; solving an eigenspectrum
problem. The Schrödinger wave equation.
</td></tr>
+
+ <tr valign="top">
+ <td><a href="../../doxygen/deal.II/step_37.html">Step-37</a></td>
+ <td> Implementing matrix-vector products without explicitly
+ storing the matrix elements (a matrix-free method).
+ </td></tr>
</table>
<tr>
<td></td>
- <td><a href="../../doxygen/deal.II/step_16.html">Step-16</a></td>
+ <td><a href="../../doxygen/deal.II/step_16.html">Step-16</a>,
+ <a href="../../doxygen/deal.II/step_37.html">Step-37</a></td>
<td> Multilevel preconditioners
</td>
</tr>
<tr valign="top">
<td><b></b></td>
<td><a href="../../doxygen/deal.II/step_16.html">Step-16</a>,
- <a href="../../doxygen/deal.II/step_31.html">Step-31</a></td>
+ <a href="../../doxygen/deal.II/step_31.html">Step-31</a>,
+ <a href="../../doxygen/deal.II/step_37.html">Step-37</a></td>
<td> Multilevel preconditioners
</td>
</tr>
If we are to perform a matrix-vector product, we can hence use that
@f{eqnarray*}
y &=& A\cdot x = \left(\sum_{\text{cell}=1}^{\mathrm{n\_cells}} P_\mathrm{cell,{loc-glob}}^T
-A_\mathrm{cell} P_\mathrm{cell,{loc-glob}}\right) \cdot x\\
+A_\mathrm{cell} P_\mathrm{cell,{loc-glob}}\right) \cdot x
+\\
&=& \sum_{\mathrm{cell}=1}^{\mathrm{n\_cells}} P_\mathrm{cell,{loc-glob}}^T
-A_\mathrm{cell} x_\mathrm{cell},
+A_\mathrm{cell} x_\mathrm{cell}
\\
&=& \sum_{\mathrm{cell}=1}^{\mathrm{n\_cells}} P_\mathrm{cell,{loc-glob}}^T
y_\mathrm{cell},