/**
* Create a view from an ArrayView itself.
*
- * This function is used for non-@p const references to objects of ArrayView type.
- * It only exists for compatibility purposes.
+ * This function is used for non-@p const references to objects of ArrayView
+ * type. It only exists for compatibility purposes.
*
* @param[in] array_view The ArrayView that we wish to make a copy of.
*
*
* *---*---*
* | 1 | 3 |
- * *---*---* case_x1y2y (successive refinement: first cut_x, then cut_y
- * for both children) | 0 | 2 |
+ * *---*---* case_x1y2y (successive refinement: first cut_x, then cut_y for both children)
+ * | 0 | 2 |
* *---*---*
*
* *-------*
*
* *---*---*
* | 2 | 3 |
- * *---*---* case_y1x2x (successive refinement: first cut_y, then cut_x
- * for both children) | 0 | 1 |
+ * *---*---* case_y1x2x (successive refinement: first cut_y, then cut_x for both children)
+ * | 0 | 1 |
* *---+---*
*
* *---*---*
* ParameterAcceptor::add_parameter() method for each parameter we want to
* have, or by constructing a ParameterAcceptorProxy class with your own class,
* provided that your class implements the @p declare_parameters and
- * @p parse_parameters functions (the first can be a static member in this case).
+ * @p parse_parameters functions (the first can be a static member in this
+ * case).
*
* By using the add_parameter method, ParameterAcceptor makes sure that the
* given parameter is registered in the global parameter handler (by calling
*
*
* @ingroup input
- * @author Wolfgang Bangerth, October 1997, revised February 1998, 2010, 2011,
- * 2017
+ * @author Wolfgang Bangerth, October 1997, revised February 1998, 2010, 2011, 2017
* @author Alberto Sartori, 2015
* @author David Wells, 2016
*/
* must be used. In case a manipulation is done that changes the roots, the
* representation is switched to the coefficient form.
*
- * @author Ralf Hartmann, Guido Kanschat, 2000, 2006, Martin Kronbichler,
- * 2011, 2017
+ * @author Ralf Hartmann, Guido Kanschat, 2000, 2006, Martin Kronbichler, 2011, 2017
*/
template <typename number>
class Polynomial : public Subscriptor
* </dl>
* where $0 \le a_1, a_2, a_3 \le k$.
*
- * @note Unlike the classical Raviart-Thomas space, the lowest order for the
- * enhanced space is 1, similarly to the Brezzi-Douglas-Marini (BDM) polynomial
- * space.
+ * @note Unlike the classical Raviart-Thomas space, the lowest order for the enhanced space
+ * is 1, similarly to the Brezzi-Douglas-Marini (BDM) polynomial space.
*
* The total dimension of the space <i>dim(V<sub>k</sub>) = d*(k+1)^d</i>, where
* <i>d</i> is the space dimension. This allows to associate shape functions
*
* @note Currently coarsening is not supported.
*
- * @note The functionality provided by this class can alternatively be
- * achieved using parallel::distributed::SolutionTransfer. However, that
- * would require the following steps: (i) create an auxiliary DoFHandler
- * with a (discontinuous Galerkin) FiniteElement which has enough components
- * to represent all data stored at the quadrature points; (ii) project the
- * data to the FiniteElement space and thereby store results in global
- * vectors; (iii) use parallel::distributed::SolutionTransfer to project FE
- * vectors to the new mesh; and (iv) finally project the data back to the
- * quadrature points on the new mesh via FEValues class. The
+ * @note The functionality provided by this class can alternatively be achieved
+ * using parallel::distributed::SolutionTransfer. However, that would
+ * require the following steps: (i) create an auxiliary DoFHandler with a
+ * (discontinuous Galerkin) FiniteElement which has enough components to
+ * represent all data stored at the quadrature points; (ii) project the data
+ * to the FiniteElement space and thereby store results in global vectors;
+ * (iii) use parallel::distributed::SolutionTransfer to project FE vectors
+ * to the new mesh; and (iv) finally project the data back to the quadrature
+ * points on the new mesh via FEValues class. The
* ContinuousQuadratureDataTransfer class aims at simplifying the whole
* process by only requiring that the quadrature point data class is derived
* from the TransferableQuadraturePointData. Everything else will be done
/**
* Prepare for coarsening and refinement of a triangulation @p tria .
- * @p data_storage represents the cell data which should be transferred and
- * it should be initialized for each locally owned active cell.
+ * @p data_storage represents the cell data which should be transferred
+ * and it should be initialized for each locally owned active cell.
*
* @note Although CellDataStorage class allows storing on different cells
* different objects derived from the base class, here we assume that
* @param[in] A The tensor of which the eigenvectors and eigenvalues are
* to be computed.
*
- * @return An array containing the eigenvectors and the associated
- * eigenvalues. The array is not sorted in any particular order.
+ * @return An array containing the eigenvectors and the associated eigenvalues.
+ * The array is not sorted in any particular order.
*
* @author Joachim Kopp, Jean-Paul Pelteret, 2017
*/
* @param[in] A The tensor of which the eigenvectors and eigenvalues are
* to be computed.
*
- * @return An array containing the eigenvectors and the associated
- * eigenvalues. The array is not sorted in any particular order.
+ * @return An array containing the eigenvectors and the associated eigenvalues.
+ * The array is not sorted in any particular order.
*
* @author Joachim Kopp, Jean-Paul Pelteret, 2017
*/
* @param[in] A The tensor of which the eigenvectors and eigenvalues are
* to be computed.
*
- * @return An array containing the eigenvectors and the associated
- * eigenvalues. The array is not sorted in any particular order.
+ * @return An array containing the eigenvectors and the associated eigenvalues.
+ * The array is not sorted in any particular order.
*
* @author Joachim Kopp, Jean-Paul Pelteret, 2017
*/
* @param[in] A The tensor of which the eigenvectors and eigenvalues are
* to be computed.
*
- * @return An array containing the eigenvectors and the associated
- * eigenvalues. The array is not sorted in any particular order.
+ * @return An array containing the eigenvectors and the associated eigenvalues.
+ * The array is not sorted in any particular order.
*
* @author Joachim Kopp, Jean-Paul Pelteret, 2017
*/
* t.return_value(); // i is now 42
* @endcode
* You will rarely have a need to write such code. On the other hand,
- * the function needs to return a writable (non-@p const) reference to support
- * code such as this:
+ * the function needs to return a writable (non-@p const) reference to
+ * support code such as this:
* @code
* std::unique_ptr<int> create_int (const std::string &s) { ... }
*
* t.return_value(); // i is now 42
* @endcode
* You will rarely have a need to write such code. On the other hand,
- * the function needs to return a writable (non-@p const) reference to support
- * code such as this:
+ * the function needs to return a writable (non-@p const) reference to
+ * support code such as this:
* @code
* std::unique_ptr<int> create_int (const std::string &s) { ... }
*
* default it is assumed that the input type does not satisfy the
* necessary conditions to construct this class.
*
- * @tparam ADNumberTrait A class that examined whether it contains the
- * necessary information to satisfy the requirements for being an
- * internally supported auto-differentiable number.
+ * @tparam ADNumberTrait A class that examined whether it contains the necessary
+ * information to satisfy the requirements for being an internally
+ * supported auto-differentiable number.
* @tparam T An arbitrary type resulting from the application of
* the SFINAE idiom to selectively specialize this class.
*
* This specialization is for the case where @p ADNumberType is an
* taped Adol-C (real) double.
*
- * @note In this case the number traits are the same as those for a taped
- * double.
+ * @note In this case the number traits are the same as those for a taped double.
*
* @author Jean-Paul Pelteret, 2017
*/
* This specialization is for the case where @p ADNumberType is an
* taped Adol-C complex double.
*
- * @note In this case the number traits are the same as those for a taped
- * complex double.
+ * @note In this case the number traits are the same as those for a taped complex
+ * double.
*
* @author Jean-Paul Pelteret, 2017
*/
* This specialization is for the case where @p ADNumberType is an
* tapeless Adol-C (real) double.
*
- * @note In this case the number traits are the same as those for a tapeless
- * double.
+ * @note In this case the number traits are the same as those for a tapeless double.
*
* @author Jean-Paul Pelteret, 2017
*/
* This function also partitions triangulation based on the MPI
* communicator provided to the constructor.
*
- * @note This function can not be used with
- * parallel::distributed::Triangulation, since it only stores those cells
- * that it owns, one layer of ghost cells around the ones it locally owns,
- * and a number of artificial cells.
+ * @note This function can not be used with parallel::distributed::Triangulation,
+ * since it only stores those cells that it owns, one layer of ghost cells
+ * around the ones it locally owns, and a number of artificial cells.
*/
virtual void
copy_triangulation(
* degrees of freedom on this cell <i>earlier</i> indices than
* all of the indices owned by processor 1.
*
- * @note This function generates an ordering that is independent of the
- * previous numbering of degrees of freedom. In other words, any information
- * that may have been produced by a previous call to a renumbering function is
+ * @note This function generates an ordering that is independent of the previous
+ * numbering of degrees of freedom. In other words, any information that may
+ * have been produced by a previous call to a renumbering function is
* ignored.
*/
template <int dim>
* @endcode
* which will result in:
*
- * | DoF | Component | Base element | Shape function within base |
- * Multiplicity | | :----: | :--------: | :----------: |
- * :------------------------: | :----------: | | 0 | 0 | 0 | 0 |
- * 0 | | 1 | 1 | 0 | 0 | 1 |
- * | 2 | 2 | 1 | 0 | 0 | | 3 |
- * 0 | 0 | 1 | 0 | | 4 | 1 |
- * 0 | 1 | 1 | | 5 | 2 | 1 |
- * 1 | 0 | | 6 | 0 | 0 | 2 | 0 |
- * | 7 | 1 | 0 | 2 | 1 | | 8 |
- * 2 | 1 | 2 | 0 | | 9 | 0 |
- * 0 | 3 | 0 | | 10 | 1 | 0 |
- * 3 | 1 | | 11 | 2 | 1 | 3 | 0 |
- * | 12 | 0 | 0 | 4 | 0 | | 13
- * | 1 | 0 | 4 | 1 | |
- * 14 | 0 | 0 | 5 | 0 |
- * | 15 | 1 | 0 | 5 | 1 | | 16
- * | 0 | 0 | 6 | 0 | |
- * 17 | 1 | 0 | 6 | 1 |
- * | 18 | 0 | 0 | 7 | 0 | | 19
- * | 1 | 0 | 7 | 1 | |
- * 20 | 0 | 0 | 8 | 0 |
- * | 21 | 1 | 0 | 8 | 1 |
+ * | DoF | Component | Base element | Shape function within base | Multiplicity |
+ * | :----: | :--------: | :----------: | :------------------------: | :----------: |
+ * | 0 | 0 | 0 | 0 | 0 |
+ * | 1 | 1 | 0 | 0 | 1 |
+ * | 2 | 2 | 1 | 0 | 0 |
+ * | 3 | 0 | 0 | 1 | 0 |
+ * | 4 | 1 | 0 | 1 | 1 |
+ * | 5 | 2 | 1 | 1 | 0 |
+ * | 6 | 0 | 0 | 2 | 0 |
+ * | 7 | 1 | 0 | 2 | 1 |
+ * | 8 | 2 | 1 | 2 | 0 |
+ * | 9 | 0 | 0 | 3 | 0 |
+ * | 10 | 1 | 0 | 3 | 1 |
+ * | 11 | 2 | 1 | 3 | 0 |
+ * | 12 | 0 | 0 | 4 | 0 |
+ * | 13 | 1 | 0 | 4 | 1 |
+ * | 14 | 0 | 0 | 5 | 0 |
+ * | 15 | 1 | 0 | 5 | 1 |
+ * | 16 | 0 | 0 | 6 | 0 |
+ * | 17 | 1 | 0 | 6 | 1 |
+ * | 18 | 0 | 0 | 7 | 0 |
+ * | 19 | 1 | 0 | 7 | 1 |
+ * | 20 | 0 | 0 | 8 | 0 |
+ * | 21 | 1 | 0 | 8 | 1 |
*
* What we see is the following: there are a total of 22 degrees-of-freedom on
* this element with components ranging from 0 to 2. Each DoF corresponds to one
* <h4>$P_0$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0000.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_0$ element,
* <h4>$P_1$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_1$ element, shape function 0 </td>
*
* <td align="center"> $P_1$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P1/P1_DGP_shape0002.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_1$ element,
* <h4>$P_2$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 0 </td>
*
* <td align="center"> $P_2$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 2 </td>
*
* <td align="center"> $P_2$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P2/P2_DGP_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 4 </td>
*
* <td align="center"> $P_2$ element, shape function 5 </td> </tr> </table>
* <h4>$P_3$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 0 </td>
*
* <td align="center"> $P_3$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 2 </td>
*
* <td align="center"> $P_3$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 4 </td>
*
* <td align="center"> $P_3$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 6 </td>
*
* <td align="center"> $P_3$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P3/P3_DGP_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 8 </td>
*
* <td align="center"> $P_3$ element, shape function 9 </td> </tr> </table>
*
*
* <h4>$P_4$ element</h4> <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 0 </td>
*
* <td align="center"> $P_4$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 2 </td>
*
* <td align="center"> $P_4$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 4 </td>
*
* <td align="center"> $P_4$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 6 </td>
*
* <td align="center"> $P_4$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 8 </td>
*
* <td align="center"> $P_4$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0011.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 10 </td>
*
* <td align="center"> $P_4$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0013.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 12 </td>
*
* <td align="center"> $P_4$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/DGP/P4/P4_DGP_shape0014.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_4$ element,
* <h4>$P_0$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0000.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_0$ element,
* <h4>$P_1$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_1$ element, shape function 0 </td>
*
* <td align="center"> $P_1$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P1/P1_DGPMonomial_shape0002.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_1$ element,
* <h4>$P_2$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 0 </td>
*
* <td align="center"> $P_2$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 2 </td>
*
* <td align="center"> $P_2$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P2/P2_DGPMonomial_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 4 </td>
*
* <td align="center"> $P_2$ element, shape function 5 </td> </tr> </table>
* <h4>$P_3$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 0 </td>
*
* <td align="center"> $P_3$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 2 </td>
*
* <td align="center"> $P_3$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 4 </td>
*
* <td align="center"> $P_3$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 6 </td>
*
* <td align="center"> $P_3$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P3/P3_DGPMonomial_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 8 </td>
*
* <td align="center"> $P_3$ element, shape function 9 </td> </tr> </table>
*
*
* <h4>$P_4$ element</h4> <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 0 </td>
*
* <td align="center"> $P_4$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 2 </td>
*
* <td align="center"> $P_4$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 4 </td>
*
* <td align="center"> $P_4$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 6 </td>
*
* <td align="center"> $P_4$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 8 </td>
*
* <td align="center"> $P_4$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0011.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 10 </td>
*
* <td align="center"> $P_4$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0013.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 12 </td>
*
* <td align="center"> $P_4$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPMonomial/P4/P4_DGPMonomial_shape0014.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_4$ element,
* <h4>$P_0$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0000.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_0$ element,
* <h4>$P_1$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_1$ element, shape function 0 </td>
*
* <td align="center"> $P_1$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P1/P1_DGPNonparametric_shape0002.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_1$ element,
* <h4>$P_2$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 0 </td>
*
* <td align="center"> $P_2$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 2 </td>
*
* <td align="center"> $P_2$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P2/P2_DGPNonparametric_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_2$ element, shape function 4 </td>
*
* <td align="center"> $P_2$ element, shape function 5 </td> </tr> </table>
* <h4>$P_3$ element</h4>
*
* <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 0 </td>
*
* <td align="center"> $P_3$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 2 </td>
*
* <td align="center"> $P_3$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 4 </td>
*
* <td align="center"> $P_3$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 6 </td>
*
* <td align="center"> $P_3$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P3/P3_DGPNonparametric_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_3$ element, shape function 8 </td>
*
* <td align="center"> $P_3$ element, shape function 9 </td> </tr> </table>
*
*
* <h4>$P_4$ element</h4> <table> <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0001.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 0 </td>
*
* <td align="center"> $P_4$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0003.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 2 </td>
*
* <td align="center"> $P_4$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0005.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 4 </td>
*
* <td align="center"> $P_4$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0007.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 6 </td>
*
* <td align="center"> $P_4$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0009.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 8 </td>
*
* <td align="center"> $P_4$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0011.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 10 </td>
*
* <td align="center"> $P_4$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0013.png
* </td> </tr> <tr> <td align="center"> $P_4$ element, shape function 12 </td>
*
* <td align="center"> $P_4$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/DGPNonparametric/P4/P4_DGPNonparametric_shape0014.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $P_4$ element,
* The variable is made mutable as InternalData's provided to fill_fe_values
* and alike are const.
*
- * @note We do not want to store this information in the finite element
- * object itself, because this would mean that (i) only one FEValues object
- * could use a finite element object at a time, and (ii) that these objects
- * could not be used in a multithreaded context.
+ * @note We do not want to store this information in the finite element object itself,
+ * because this would mean that (i) only one FEValues object could use a
+ * finite element object at a time, and (ii) that these objects could not be
+ * used in a multithreaded context.
*/
mutable std::vector<std::vector<EnrichmentValues>> enrichment;
};
/**
* For each finite element @p i used in enrichment and each enrichment function
* @p j associated with it (essentially its multiplicity),
- * @p base_no_mult_local_enriched_dofs[i][j] contains the associated local DoFs
- * on the FE_Enriched finite element.
+ * @p base_no_mult_local_enriched_dofs[i][j] contains the associated local
+ * DoFs on the FE_Enriched finite element.
*/
std::vector<std::vector<std::vector<unsigned int>>>
base_no_mult_local_enriched_dofs;
* <ul>
* <li> $\lambda_{i}$ - trilinear function, equal to one at the $i$-th vertex
* and zero at all other vertices.</li>
- * <li> $\sigma_{i}$ - linear functional associated with the $i$-th
- * vertex.</li>
+ * <li> $\sigma_{i}$ - linear functional associated with the $i$-th vertex.</li>
* </ul>
*
* The definitions of these functionals, as well as the edge and face
*
* In 2d, these shape functions look as follows: <table> <tr> <td
* align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_1$ element, shape function 0 </td>
*
* <td align="center"> $Q_1$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q1/Q1_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_1$ element, shape function 2 </td>
*
* <td align="center"> $Q_1$ element, shape function 3 </td> </tr> </table>
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_2$ element, shape function 0 </td>
*
* <td align="center"> $Q_2$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_2$ element, shape function 2 </td>
*
* <td align="center"> $Q_2$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_2$ element, shape function 4 </td>
*
* <td align="center"> $Q_2$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_2$ element, shape function 6 </td>
*
* <td align="center"> $Q_2$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q2/Q2_shape0008.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $Q_2$ element,
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 0 </td>
*
* <td align="center"> $Q_3$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 2 </td>
*
* <td align="center"> $Q_3$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 4 </td>
*
* <td align="center"> $Q_3$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 6 </td>
*
* <td align="center"> $Q_3$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0009.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 8 </td>
*
* <td align="center"> $Q_3$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0011.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 10 </td>
*
* <td align="center"> $Q_3$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0013.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 12 </td>
*
* <td align="center"> $Q_3$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0014.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0015.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q3/Q3_shape0015.png
* </td> </tr> <tr> <td align="center"> $Q_3$ element, shape function 14 </td>
*
* <td align="center"> $Q_3$ element, shape function 15 </td> </tr> </table>
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 0 </td>
*
* <td align="center"> $Q_4$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 2 </td>
*
* <td align="center"> $Q_4$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 4 </td>
*
* <td align="center"> $Q_4$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 6 </td>
*
* <td align="center"> $Q_4$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0009.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 8 </td>
*
* <td align="center"> $Q_4$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0011.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 10 </td>
*
* <td align="center"> $Q_4$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0013.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 12 </td>
*
* <td align="center"> $Q_4$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0014.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0015.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0015.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 14 </td>
*
* <td align="center"> $Q_4$ element, shape function 15 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0016.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0016.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0017.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0017.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 16 </td>
*
* <td align="center"> $Q_4$ element, shape function 17 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0018.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0018.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0019.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0019.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 18 </td>
*
* <td align="center"> $Q_4$ element, shape function 19 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0020.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0020.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0021.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0021.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 20 </td>
*
* <td align="center"> $Q_4$ element, shape function 21 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0022.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0022.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0023.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0023.png
* </td> </tr> <tr> <td align="center"> $Q_4$ element, shape function 22 </td>
*
* <td align="center"> $Q_4$ element, shape function 23 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0024.png
+ * @image html http://www.dealii.org/images/shape-functions/lagrange/Q4/Q4_shape0024.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $Q_4$ element,
*
* In 2d, these shape functions look as follows: <table> <tr> <td
* align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_1^H$ element, shape function 0
* </td>
*
* <td align="center"> $Q_1^H$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q1/Q1H_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_1^H$ element, shape function 2
* </td>
*
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_2^H$ element, shape function 0
* </td>
*
* <td align="center"> $Q_2^H$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_2^H$ element, shape function 2
* </td>
*
* <td align="center"> $Q_2^H$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_2^H$ element, shape function 4
* </td>
*
* <td align="center"> $Q_2^H$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_2^H$ element, shape function 6
* </td>
*
* <td align="center"> $Q_2^H$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q2/Q2H_shape0008.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $Q_2^H$ element,
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 0
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 2
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 4
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 6
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0009.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 8
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0011.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 10
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0013.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 12
* </td>
*
* <td align="center"> $Q_3^H$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0014.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0015.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q3/Q3H_shape0015.png
* </td> </tr> <tr> <td align="center"> $Q_3^H$ element, shape function 14
* </td>
*
* In 2d, these shape functions look as follows (the black plane corresponds
* to zero; negative shape function values may not be visible): <table> <tr>
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0000.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0000.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0001.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0001.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 0
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 1 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0002.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0002.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0003.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0003.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 2
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 3 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0004.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0004.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0005.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0005.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 4
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 5 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0006.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0006.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0007.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0007.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 6
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 7 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0008.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0008.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0009.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0009.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 8
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 9 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0010.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0010.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0011.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0011.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 10
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 11 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0012.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0012.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0013.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0013.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 12
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 13 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0014.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0014.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0015.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0015.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 14
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 15 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0016.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0016.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0017.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0017.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 16
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 17 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0018.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0018.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0019.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0019.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 18
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 19 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0020.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0020.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0021.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0021.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 20
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 21 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0022.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0022.png
* </td>
*
* <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0023.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0023.png
* </td> </tr> <tr> <td align="center"> $Q_4^H$ element, shape function 22
* </td>
*
* <td align="center"> $Q_4^H$ element, shape function 23 </td> </tr>
*
* <tr> <td align="center">
- * @image html
- * http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0024.png
+ * @image html http://www.dealii.org/images/shape-functions/hierarchical/Q4/Q4H_shape0024.png
* </td>
*
* <td align="center"> </td> </tr> <tr> <td align="center"> $Q_4^H$ element,
* solution and stabilization techniques are used that work for linears but
* not higher order elements. </li>
*
- * <li> Stokes/Navier Stokes systems such as the one discussed in step-22 could
- * be solved with Q2-iso-Q1 elements for velocities instead of Q2 elements.
+ * <li> Stokes/Navier Stokes systems such as the one discussed in step-22 could be
+ * solved with Q2-iso-Q1 elements for velocities instead of Q2 elements.
* Combined with Q1 pressures they give a stable mixed element pair. However,
* they perform worse than the standard (Taylor-Hood $Q_2\times Q_1$)
* approach in most situations. </li>
* @p predicate being constant. Return the pair of vectors of predicate values
* and the vector of calculated subset norms.
*
- * @p predicate should return a pair of <code>bool</code> and <code>unsigned int</code>.
- * The former is a flag whether a given TableIndices should be used in
- * calculation, whereas the latter is the unrolled value of indices according
- * to which the subsets of coefficients will be formed.
+ * @p predicate should return a pair of <code>bool</code> and <code>unsigned
+ * int</code>. The former is a flag whether a given TableIndices should be
+ * used in calculation, whereas the latter is the unrolled value of indices
+ * according to which the subsets of coefficients will be formed.
*
* @note Only the following values of @p norm are implemented and make sense
* in this case: mean, L1_norm, L2_norm, Linfty_norm. The mean norm can only
* cells. See hyper_rectangle(), if different lengths in different ordinate
* directions are required.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim, int spacedim>
void
* dimensional space with the remaining entries set to zero. For example, a
* <tt>Triangulation@<2,3@></tt> will be a square in the xy plane with z=0.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim, int spacedim>
void
* <tt>Triangulation@<2,3@></tt> will be a rectangle in the xy plane with
* z=0, defined by the two opposing corners @p p1 and @p p2.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim, int spacedim>
void
*
* @note This function is implemented in 2d only.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* vertices in the array of <code>corners</code> will no longer refer to the
* same triangulation.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* of subdivisions in each of the @p dim directions. Colorizing is done
* according to hyper_rectangle().
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* number of subdivisions in each of the @p dim directions may vary.
* Colorizing is done according to hyper_rectangle().
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
*
* Presently only available in 2d and 3d.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* SphericalManifold manifold also to the boundary cells, and not only to the
* boundary faces.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* @image html sphere.png
* @image html sphere_section.png
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int spacedim>
* boundary and 1 for the cut plane. The manifold id for the curved boundary
* is set to zero, and a SphericalManifold is attached to it.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* The manifold id for the hull of the cylinder is set to zero, and a
* CylindricalManifold is attached to it.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* In three dimensions, the manifold id of the hull is set to zero, and a
* CylindricalManifold is attached to it.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*
* @author Markus Bürg, 2009
*/
* This function exists for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* If @p colorize is set to @p true, the faces forming the slit are marked
* with boundary id 1 and 2, respectively.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* @note This function is declared to exist for triangulations of all space
* dimensions, but throws an error if called in 1d.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* All manifold ids are set to zero, and a SphericalManifold is attached
* to the triangulation.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* All manifold ids are set to zero, and a SphericalManifold is attached
* to the triangulation.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* All manifold ids are set to zero, and a CylindricalManifold is attached
* to the triangulation.
*
- * @note The triangulation passed as argument needs to be empty when calling
- * this function.
+ * @note The triangulation passed as argument needs to be empty when calling this function.
*/
template <int dim>
void
* If @p points[a] and @p points[b] are the only two points that fall in @p cells[c],
* then @p qpoints[c][0] and @p qpoints[c][1] are the reference positions of
* @p points[a] and @p points[b] in @p cells[c], and @p indices[c][0] = a,
- * @p indices[c][1] = b. The function Mapping::transform_unit_to_real(qpoints[c][0])
+ * @p indices[c][1] = b. The function
+ * Mapping::transform_unit_to_real(qpoints[c][0])
* returns @p points[a].
*
* The algorithm assumes it's easier to look for a point in the cell that was
/**
* Given a @p cache and a list of
- * @p local_points for each process, find the points lying on the locally owned
- * part of the mesh and compute the quadrature rules for them.
+ * @p local_points for each process, find the points lying on the locally
+ * owned part of the mesh and compute the quadrature rules for them.
* Distributed compute point locations is a function similar to
* GridTools::compute_point_locations but working for parallel::Triangulation
* objects and, unlike its serial version, also for a distributed
* If @p max_boxes was left as default or bigger than 1 these two boxes would be returned.
* - 4. Because @p max_boxes = 1 the smallest bounding box is merged to the bigger one.
* Notice it is important to choose the parameters wisely. For instance, @p allow_merge = false and
- * @p refinement_level = 1 returns the very same bounding box but with a fraction of the computational cost.
+ * @p refinement_level = 1 returns the very same bounding box but with a
+ * fraction of the computational cost.
*
* This function does not take into account the curvature of cells and thus it
* is not suited for handling curved geometry: the mapping is assumed to be
* between the two points in ${\mathbb R}^d$.
*
*
- * @note Unlike almost all other cases in the library, we here interpret the
- * points to be in real space, not on the reference cell.
+ * @note Unlike almost all other cases in the library, we here interpret the points
+ * to be in real space, not on the reference cell.
*
* Manifold::get_new_point() has a default implementation that can
* simplify this process somewhat: Internally, the function calls the
* @ref step_36 "step-36"
* for an example.
*
- * @author Baerbel Janssen, Agnieszka Miedlar, 2010, Guido Kanschat 2015, Joscha
- * Gedicke 2016
+ * @author Baerbel Janssen, Agnieszka Miedlar, 2010, Guido Kanschat 2015, Joscha Gedicke 2016
*/
class ArpackSolver : public Subscriptor
{
* @note It is assumed that @p A, @p B and @p V have compatible sizes and that
* @p C already has the right size.
*
- * @note This function is not provided by LAPACK. The function first forms
- * $\rm{diag}(\mathbf V) \cdot \mathbf B$ product and then uses Xgemm
- * function.
+ * @note This function is not provided by LAPACK. The function first forms $\rm{diag}(\mathbf V) \cdot \mathbf B$ product and
+ * then uses Xgemm function.
*/
void
Tmmult(LAPACKFullMatrix<number> & C,
* Compute the Cholesky factorization of the matrix using LAPACK function
* Xpotrf.
*
- * @note The factorization is stored in the lower-triangular part of the
- * matrix.
+ * @note The factorization is stored in the lower-triangular part of the matrix.
*/
void
compute_cholesky_factorization();
* positive definite matrix using Cholesky factorization. This function can
* only be called if the matrix is already factorized.
*
- * @note The condition number $k(\mathbf A)$ can be used to estimate the
- * numerical error related to the matrix inversion or the solution of the
+ * @note The condition number $k(\mathbf A)$ can be used to estimate the numerical
+ * error related to the matrix inversion or the solution of the
* system of linear algebraic equations as
* <code>error = std::numeric_limits<Number>::epsilon * k</code>.
* Alternatively one can get the number of accurate digits
*
* If this function is not called, the shift is assumed to be zero.
*
- * @note only relevant for <code>mode=3</code> (see the general documentation
- * of this class for a definition of what the different modes are).
+ * @note only relevant for <code>mode=3</code> (see the general documentation of this
+ * class for a definition of what the different modes are).
*/
void
set_shift(const std::complex<double> sigma);
* way, the ghost parameter can equal the set of locally relevant
* degrees of freedom, see step-32.
*
- * @note This operation always creates a ghosted vector, which is
- * considered read-only.
+ * @note This operation always creates a ghosted vector, which is considered
+ * read-only.
*
* @see
* @ref GlossGhostedVector "vectors with ghost elements"
* };
* @endcode
*
- * @note This function requires that the header
- * read_write_vector.templates.h be included.
+ * @note This function requires that the header read_write_vector.templates.h
+ * be included.
*/
template <typename Functor>
void
* The operations based on the input parameter @p transpose_B and the
* alignment conditions are summarized in the following table:
*
- * | transpose_B | Block Sizes | Operation
- * | | :---------: | :--------------------------: |
- * :-------------------------------------------: | | false | $MB_A=MB_B$
- * <br> $NB_A=NB_B$ | $\mathbf{A} = a \mathbf{A} + b \mathbf{B}$ | | true
- * | $MB_A=NB_B$ <br> $NB_A=MB_B$ | $\mathbf{A} = a \mathbf{A} + b
- * \mathbf{B}^T$ |
+ * | transpose_B | Block Sizes | Operation |
+ * | :---------: | :--------------------------: | :-------------------------------------------: |
+ * | false | $MB_A=MB_B$ <br> $NB_A=NB_B$ | $\mathbf{A} = a \mathbf{A} + b \mathbf{B}$ |
+ * | true | $MB_A=NB_B$ <br> $NB_A=MB_B$ | $\mathbf{A} = a \mathbf{A} + b \mathbf{B}^T$ |
*
* The matrices $\mathbf{A}$ and $\mathbf{B}$ must have the same process grid.
*/
* The operations based on the input parameters and the alignment conditions
* are summarized in the following table:
*
- * | transpose_A | transpose_B | Block Sizes | Operation | |
- * :---------: | :---------: | :-------------------------------------------: |
- * :-------------------------------------------------------------: | | false
- * | false | $MB_A=MB_C$ <br> $NB_A=MB_B$ <br> $NB_B=NB_C$ | $\mathbf{C}
- * = b \mathbf{A} \cdot \mathbf{B} + c \mathbf{C}$ | | false | true
- * | $MB_A=MB_C$ <br> $NB_A=NB_B$ <br> $MB_B=NB_C$ | $\mathbf{C} = b
- * \mathbf{A} \cdot \mathbf{B}^T + c \mathbf{C}$ | | true | false |
- * $MB_A=MB_B$ <br> $NB_A=MB_C$ <br> $NB_B=NB_C$ | $\mathbf{C} = b
- * \mathbf{A}^T \cdot \mathbf{B} + c \mathbf{C}$ | | true | true |
- * $MB_A=NB_B$ <br> $NB_A=MB_C$ <br> $MB_B=NB_C$ | $\mathbf{C} = b
- * \mathbf{A}^T \cdot \mathbf{B}^T + c \mathbf{C}$ |
+ * | transpose_A | transpose_B | Block Sizes | Operation |
+ * | :---------: | :---------: | :-------------------------------------------: | :-------------------------------------------------------------: |
+ * | false | false | $MB_A=MB_C$ <br> $NB_A=MB_B$ <br> $NB_B=NB_C$ | $\mathbf{C} = b \mathbf{A} \cdot \mathbf{B} + c \mathbf{C}$ |
+ * | false | true | $MB_A=MB_C$ <br> $NB_A=NB_B$ <br> $MB_B=NB_C$ | $\mathbf{C} = b \mathbf{A} \cdot \mathbf{B}^T + c \mathbf{C}$ |
+ * | true | false | $MB_A=MB_B$ <br> $NB_A=MB_C$ <br> $NB_B=NB_C$ | $\mathbf{C} = b \mathbf{A}^T \cdot \mathbf{B} + c \mathbf{C}$ |
+ * | true | true | $MB_A=NB_B$ <br> $NB_A=MB_C$ <br> $MB_B=NB_C$ | $\mathbf{C} = b \mathbf{A}^T \cdot \mathbf{B}^T + c \mathbf{C}$ |
*
* It is assumed that $\mathbf{A}$ and $\mathbf{B}$ have compatible sizes and
* that
*
* If successful, the computed eigenvalues are arranged in ascending order.
*
- * @note Due to a bug in Netlib-ScaLAPACK, either all or no eigenvectors can
- * be computed.
+ * @note Due to a bug in Netlib-ScaLAPACK, either all or no eigenvectors can be computed.
* Therefore, the input @p index_limits has to be set accordingly. Using Intel-MKL this restriction is not required.
*/
std::vector<NumberType>
* It is not required that the matrices A and B have the same process grid or
* block size, e.g. copying a matrix from a one-dimensional to a
* two-dimensional process grid
- * @p ictxt is a context which is at least a union of all processes in context A and B
+ * @p ictxt is a context which is at least a union of all processes in context
+ * A and B
*/
void
pdgemr2d_(const int * m,
* @tparam dim Dimension of the problem. Currently, 1D, 2D, and 3D codes are
* implemented.
*
- * @tparam Number Arithmetic type of the underlying array elements. Note that
- * the underlying LAPACK implementation supports only float and double numbers,
- * so only these two types are currently supported by the generic class.
+ * @tparam Number Arithmetic type of the underlying array elements. Note that the
+ * underlying LAPACK implementation supports only float and double numbers, so
+ * only these two types are currently supported by the generic class.
* Nevertheless, a template specialization for the vectorized types
* VectorizedArray<float> and VectorizedArray<double> exists. This is necessary
* to perform LAPACK calculations for each vectorization lane, i.e. for the
* except for the higher_order_elements parameter which does not exist in
* PreconditionerAMGMueLu.
*
- * @note This class requires Trilinos 11.14 or higher. At the moment
- * 64bit-indices are not supported.
+ * @note This class requires Trilinos 11.14 or higher. At the moment 64bit-indices
+ * are not supported.
*
* @warning This interface should not be considered as stable.
*
*
* @tparam dim Dimension in which this class is to be used
*
- * @tparam fe_degree Degree of the tensor prodict finite element with
- * fe_degree+1 degrees of freedom per coordinate direction
+ * @tparam fe_degree Degree of the tensor prodict finite element with fe_degree+1
+ * degrees of freedom per coordinate direction
*
* @tparam n_q_points_1d Number of points in the quadrature formular in 1D,
* defaults to fe_degree+1
* @tparam variant Variant of evaluation used for creating template
* specializations
* @tparam dim Dimension of the function
- * @tparam n_rows Number of rows in the transformation matrix, which
- * corresponds to the number of 1d shape functions in the usual tensor
+ * @tparam n_rows Number of rows in the transformation matrix, which corresponds
+ * to the number of 1d shape functions in the usual tensor
* contraction setting
* @tparam n_columns Number of columns in the transformation matrix, which
* corresponds to the number of 1d shape functions in the
* tensor product form of the basis functions.
*
* @tparam dim Space dimension in which this class is applied
- * @tparam n_rows Number of rows in the transformation matrix, which
- * corresponds to the number of 1d shape functions in the usual tensor
+ * @tparam n_rows Number of rows in the transformation matrix, which corresponds
+ * to the number of 1d shape functions in the usual tensor
* contraction setting
* @tparam n_columns Number of columns in the transformation matrix, which
* corresponds to the number of 1d shape functions in the
* before calling any interpolation within the face.
*
* @tparam face_direction Direction of the normal vector (0=x, 1=y, etc)
- * @tparam contract_onto_face If true, the input vector is of size
- * n_rows^dim and interpolation into n_rows^(dim-1) points is performed.
- * This is a typical scenario in FEFaceEvaluation::evaluate() calls. If
- * false, data from n_rows^(dim-1) points is expanded into the n_rows^dim
- * points of the higher- dimensional data array. Derivatives in the case
- * contract_onto_face==false are summed together
+ * @tparam contract_onto_face If true, the input vector is of size n_rows^dim
+ * and interpolation into n_rows^(dim-1) points
+ * is performed. This is a typical scenario in
+ * FEFaceEvaluation::evaluate() calls. If false,
+ * data from n_rows^(dim-1) points is expanded
+ * into the n_rows^dim points of the higher-
+ * dimensional data array. Derivatives in the
+ * case contract_onto_face==false are summed
+ * together
* @tparam add If true, the result is added to the output vector, else
* the computed values overwrite the content in the output
* @tparam max_derivative Sets the number of derivatives that should be
* are, too.
*
* @tparam dim Space dimension in which this class is applied
- * @tparam n_rows Number of rows in the transformation matrix, which
- * corresponds to the number of 1d shape functions in the usual tensor
+ * @tparam n_rows Number of rows in the transformation matrix, which corresponds
+ * to the number of 1d shape functions in the usual tensor
* contraction setting
* @tparam n_columns Number of columns in the transformation matrix, which
* corresponds to the number of 1d shape functions in the
* constants (templates).
*
* @tparam dim Space dimension in which this class is applied
- * @tparam n_rows Number of rows in the transformation matrix, which
- * corresponds to the number of 1d shape functions in the usual tensor
+ * @tparam n_rows Number of rows in the transformation matrix, which corresponds
+ * to the number of 1d shape functions in the usual tensor
* contraction setting
* @tparam n_columns Number of columns in the transformation matrix, which
* corresponds to the number of 1d shape functions in the
* difference is in the way the input and output quantities are symmetrized.
*
* @tparam dim Space dimension in which this class is applied
- * @tparam n_rows Number of rows in the transformation matrix, which
- * corresponds to the number of 1d shape functions in the usual tensor
+ * @tparam n_rows Number of rows in the transformation matrix, which corresponds
+ * to the number of 1d shape functions in the usual tensor
* contraction setting
* @tparam n_columns Number of columns in the transformation matrix, which
* corresponds to the number of 1d shape functions in the
* the same principles of WorkStream::run. Internally the function passes to
* @p boundary_worker, in addition to the above, also a @p face_no parameter
* that identifies the face on which the integration should be performed. The
- * @p face_worker instead needs to identify the current face unambiguously both on
- * the cell and on the neighboring cell, and it is therefore called with six
- * arguments (three for each cell: the actual cell, the face index, and
- * the subface_index. If no subface integration is needed, then the
+ * @p face_worker instead needs to identify the current face unambiguously
+ * both on the cell and on the neighboring cell, and it is therefore called
+ * with six arguments (three for each cell: the actual cell, the face index,
+ * and the subface_index. If no subface integration is needed, then the
* subface_index is numbers::invalid_unsigned_int) in addition to the usual
* ScratchData and CopyData objects.
*
* constrains degrees on the external boundary of the domain by calling
* MGTools::make_boundary_list() with the given second and third argument.
*
- * @deprecated Use initialize() followed by make_zero_boundary_constraints()
- * instead
+ * @deprecated Use initialize() followed by make_zero_boundary_constraints() instead
*/
template <int dim, int spacedim>
DEAL_II_DEPRECATED void
struct Signals
{
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to MGTransfer::copy_to_mg which transfers the vector
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to MGTransfer::copy_to_mg which transfers the vector
* given to it to a multi-level vector.
*/
boost::signals2::signal<void(const bool before)> transfer_to_mg;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to MGTransfer::copy_from_mg which transfers the
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to MGTransfer::copy_from_mg which transfers the
* multi-level vector given to it to a normal vector.
*/
boost::signals2::signal<void(const bool before)> transfer_to_global;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is
* false) the call to the coarse solver on @p level.
*/
boost::signals2::signal<void(const bool before, const unsigned int level)>
coarse_solve;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to MGTransfer::restrict_and_add() which restricts a
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to MGTransfer::restrict_and_add() which restricts a
* vector from @p level to the next coarser one (@p level - 1).
*/
boost::signals2::signal<void(const bool before, const unsigned int level)>
restriction;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to MGTransfer::prolongate() which prolongs a vector to
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to MGTransfer::prolongate() which prolongs a vector to
* @p level from the next coarser one (@p level - 1).
*/
boost::signals2::signal<void(const bool before, const unsigned int level)>
prolongation;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to a pre-smoothing step via MGPreSmoother::apply() on
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to a pre-smoothing step via MGPreSmoother::apply() on
* @p level.
*/
boost::signals2::signal<void(const bool before, const unsigned int level)>
pre_smoother_step;
/**
- * This signal is triggered before (@p before is true) and after (@p before is
- * false) the call to a post-smoothing step via MGPostSmoother::apply() on
+ * This signal is triggered before (@p before is true) and after (@p before
+ * is false) the call to a post-smoothing step via MGPostSmoother::apply()
+ * on
* @p level.
*/
boost::signals2::signal<void(const bool before, const unsigned int level)>
* // like above, but now also make sure that DataOut provides
* // us with coordinates of the evaluation points:
* DataPostprocessorVector<dim> ("heat_flux",
- * update_gradients |
- * update_quadrature_points)
+ * update_gradients | update_quadrature_points)
* {}
*
* virtual
* function multiple times with only one boundary indicator, or whether we
* call the function once with the whole set of boundary indicators at once.
*
- * Argument four (@p function_map) describes the boundary function $\vec u_\Gamma$
- * for each boundary id. The function <code>function_map[id]</code>
+ * Argument four (@p function_map) describes the boundary function $\vec
+ * u_\Gamma$ for each boundary id. The function <code>function_map[id]</code>
* is used on boundary with id @p id taken from the set @p boundary_ids.
* Each function in @p function_map is expected to have @p dim
* components, which are used independent of @p first_vector_component.
*
* @author Luca Heltai, Andrea Mola, 2011--2014.
*
- * @deprecated Use DirectionalProjectionManifold instead, which is identical
- * to this class but satisfies the modern Manifold-based naming convention.
+ * @deprecated Use DirectionalProjectionManifold instead, which is identical to
+ * this class but satisfies the modern Manifold-based naming convention.
*/
template <int dim, int spacedim>
class DEAL_II_DEPRECATED DirectionalProjectionBoundary
*
* @author Luca Heltai, Andrea Mola, 2011--2014.
*
- * @deprecated Use NormalToMeshProjectionManifold instead, which is identical
- * to this class but satisfies the modern Manifold-based naming convention.
+ * @deprecated Use NormalToMeshProjectionManifold instead, which is identical to
+ * this class but satisfies the modern Manifold-based naming convention.
*/
template <int dim, int spacedim>
class DEAL_II_DEPRECATED NormalToMeshProjectionBoundary
* $\mathcal{S}$ introduced in the Physics::Elasticity namespace
* description and that which is returned by identity_tensor().
*
- * @note If you apply this to a standard tensor then it doesn't behave
- * like the fourth-order identity tensor, but rather as a symmetrization
+ * @note If you apply this to a standard tensor then it doesn't behave like
+ * the fourth-order identity tensor, but rather as a symmetrization
* operator.
*/
static const SymmetricTensor<4, dim> S;
* \hat{\mathcal{P}} \equiv \hat{\mathcal{P}}^{T} : \bar{\mathbf{S}} \, .
* @f]
*
- * @note Comparing the definition of this tensor in Holzapfel (2001) to
- * that adopted here, the inclusion of the extra factor
- * $J^{-2/\textrm{dim}}$ does not, at the outset, seem to be a reasonable
- * choice. However, in the author's view it makes direct implementation of
- * the expressions for isochoric (referential) stress contributions and
- * their linearization simpler in practise.
+ * @note Comparing the definition of this tensor in Holzapfel (2001) to that
+ * adopted here, the inclusion of the extra factor $J^{-2/\textrm{dim}}$
+ * does not, at the outset, seem to be a reasonable choice. However, in
+ * the author's view it makes direct implementation of the expressions for
+ * isochoric (referential) stress contributions and their linearization
+ * simpler in practise.
*
* @dealiiWriggersA{46,3.125}
* @dealiiHolzapfelA{229,6.83}
*
* @precondition: face_1 is supposed to be active
*
- * @note As bug #82 ((http://code.google.com/p/dealii/issues/detail?id=82)
- * and the corresponding testcase bits/periodicity_05 demonstrate, we can
+ * @note As bug #82 ((http://code.google.com/p/dealii/issues/detail?id=82) and the
+ * corresponding testcase bits/periodicity_05 demonstrate, we can
* occasionally get into trouble if we already have the constraint x1=x2 and
* want to insert x2=x1. we avoid this by skipping an identity constraint if
* the opposite constraint already exists
{
/**
* Depending on what information is called for in the update flags of the
- * @p data object, compute the various pieces of information that is required
- * by the fill_fe_face_values() and fill_fe_subface_values() functions.
- * This function simply unifies the work that would be done by
+ * @p data object, compute the various pieces of information that is
+ * required by the fill_fe_face_values() and fill_fe_subface_values()
+ * functions. This function simply unifies the work that would be done by
* those two functions.
*
* The resulting data is put into the @p output_data argument.
{
/**
* Depending on what information is called for in the update flags of the
- * @p data object, compute the various pieces of information that is required
- * by the fill_fe_face_values() and fill_fe_subface_values() functions.
- * This function simply unifies the work that would be done by
+ * @p data object, compute the various pieces of information that is
+ * required by the fill_fe_face_values() and fill_fe_subface_values()
+ * functions. This function simply unifies the work that would be done by
* those two functions.
*
* The resulting data is put into the @p output_data argument.
// / /
// / /
// *---------------*
- // | | | | | | | |
- // | | | | / | |/
+ // | |
+ // | |
+ // | |
+ // | |
+ // | |
+ // | | /
+ // | |/
// *---------------*
//
//
// / /
// / /
// *---------------*
- // | | | | / | |/
+ // | |
+ // | | /
+ // | |/
// *---------------*
- // | | | | / | |/
+ // | |
+ // | | /
+ // | |/
// *---------------*
//
//
// / / /
// / / /
// *-------*-------*
- // | | | | |
- // | / | | |/
+ // | | |
+ // | | | /
+ // | | |/
// *-------*-------*
- // | | | | |
- // | / | | |/
+ // | | |
+ // | | | /
+ // | | |/
// *-------*-------*
//
//
// / / /
// / / /
// *-------*-------*
- // | | | | |
- // | / | | |/
+ // | | |
+ // | | | /
+ // | | |/
// *-------*-------*
- // | | | | |
- // | / | | |/
+ // | | |
+ // | | | /
+ // | | |/
// *-------*-------*
//
//
projects / dealii.git / commitdiff