#endif
/**
- * Specify the constraints which the
- * dofs on the two sides of a cell interface
- * underly if the line connects two
- * cells of which one is refined once.
+ * Specify the constraints which
+ * the dofs on the two sides of a
+ * cell interface underly if the
+ * line connects two cells of
+ * which one is refined once.
*
- * For further details see the general
- * description of the derived class.
+ * For further details see the
+ * general description of the
+ * derived class.
*
- * This field is obviously useless in one
- * space dimension.
+ * This field is obviously
+ * useless in one space dimension
+ * and has there a zero size.
*/
FullMatrix<double> interface_constraints;
/**
- * Map between linear dofs and component dofs.
+ * Map between linear dofs and
+ * component dofs.
*/
vector< pair<unsigned int, unsigned int> > system_to_component_table;
/**
- * Map between linear dofs and component dofs on face.
+ * Map between linear dofs and
+ * component dofs on face.
*/
vector< pair<unsigned int, unsigned int> > face_system_to_component_table;
/**
- * Map between component and linear dofs.
+ * Map between component and
+ * linear dofs.
*/
vector< vector<unsigned int> > component_to_system_table;
/**
- * Map between component and linear dofs on a face.
+ * Map between component and
+ * linear dofs on a face.
*/
vector< vector<unsigned int> > face_component_to_system_table;
+
/**
- * The base element establishing a
- * component.
+ * The base element establishing
+ * a component.
*
* This table converts a
* component number to the
vector<unsigned int> component_to_base_table;
/**
- * This flag determines how the restriction
- * of data from child cells to its mother
- * is to be done. In this, it also
- * determines in which way the restriction
- * matrices of the derived class are to
- * be used.
- *
- * For most elements, the mode is the
- * following. Consider a 1d linear element,
- * with two children and nodal values
- * 1 and 2 on the first child, and 2 and 4
- * on the second child. The restriction
- * to the mother child then yields the
- * values 1 and four, i.e. the values on
- * the mother cell can be obtained by
- * pointwise interpolation, where for each
- * nodal value on the mother child one
- * point on exactly one child exists.
- * However, already on the quadratic
- * element, the midpoint on the mother
- * element can be obtained from any of
- * the two children, which however would
- * both yield the same value due to
- * continuity. What we do in practice
- * is to compute them from both sides
- * and set them, rather than add them up.
- * This makes some things much easier. In
- * practice, if a degree of freedom on
- * one of the child cells yields a
- * nonzero contribution to one of the
- * degrees of freedom on the mother
- * cell, we overwrite the value on
- * the mother cell. This way, when setting
- * up the restriction matrices, we do not
- * have to track which child is responsible
- * for setting a given value on the mother
- * cell. We call this the non-additive
- * mode.
- *
- * The other possibility would be to
- * add up the contributions from the
- * different children. This would mean
- * that both of the inner endpoint of
- * the quadratic child elements above
- * would have a weight of 1/2 with
- * respect to the midpoint value on
- * the mother cell. However, this also
- * means that we have to first compute
- * the restriction to the mother cell
- * by addition from the child cells, and
- * afterwards set them to the global
- * vector. The same process, adding
- * up the local contributions to the
- * global vector is not possible since
- * we do not know how many coarse cells
- * contribute to nodes on the boundary.
- *
- * In contrast to the non-additive mode
- * described above, which is the simplest
- * way for elements can be interpolated
- * from its children, interpolation is
- * not possible for piecewise constant
- * elements, to name only one example.
- * Here, the value on the mother cell
- * has to be taken the average of the
- * values on the children, i.e. all
- * children contribute alike to the
- * one degree of freedom. Here, we have
- * to sum up the contributions of all
- * child cells with the same weight,
- * and the non-additive mode of above
- * would only set the value on the mother
- * cell to the value of one of the child
- * cell, irrespective of the values on the
- * other cells.
- *
- * Similarly, for discontinuous linear
- * elements, it might be better to not
- * interpolate the values at the corners
- * from the child cells, but to take a
+ * This flag determines how the
+ * restriction of data from child
+ * cells to its mother is to be
+ * done. In this, it also
+ * determines in which way the
+ * restriction matrices of the
+ * derived class are to be used.
+ *
+ * For most elements, the mode is
+ * the following. Consider a 1d
+ * linear element, with two
+ * children and nodal values 1
+ * and 2 on the first child, and
+ * 2 and 4 on the second
+ * child. The restriction to the
+ * mother child then yields the
+ * values 1 and four, i.e. the
+ * values on the mother cell can
+ * be obtained by pointwise
+ * interpolation, where for each
+ * nodal value on the mother
+ * child one point on exactly one
+ * child exists. However,
+ * already on the quadratic
+ * element, the midpoint on the
+ * mother element can be obtained
+ * from any of the two children,
+ * which however would both yield
+ * the same value due to
+ * continuity. What we do in
+ * practice is to compute them
+ * from both sides and set them,
+ * rather than add them up. This
+ * makes some things much
+ * easier. In practice, if a
+ * degree of freedom on one of
+ * the child cells yields a
+ * nonzero contribution to one of
+ * the degrees of freedom on the
+ * mother cell, we overwrite the
+ * value on the mother cell. This
+ * way, when setting up the
+ * restriction matrices, we do
+ * not have to track which child
+ * is responsible for setting a
+ * given value on the mother
+ * cell. We call this the
+ * non-additive mode.
+ *
+ * The other possibility would be
+ * to add up the contributions
+ * from the different
+ * children. This would mean that
+ * both of the inner endpoint of
+ * the quadratic child elements
+ * above would have a weight of
+ * 1/2 with respect to the
+ * midpoint value on the mother
+ * cell. However, this also means
+ * that we have to first compute
+ * the restriction to the mother
+ * cell by addition from the
+ * child cells, and afterwards
+ * set them to the global
+ * vector. The same process,
+ * adding up the local
+ * contributions to the global
+ * vector is not possible since
+ * we do not know how many coarse
+ * cells contribute to nodes on
+ * the boundary.
+ *
+ * In contrast to the
+ * non-additive mode described
+ * above, which is the simplest
+ * way for elements can be
+ * interpolated from its
+ * children, interpolation is not
+ * possible for piecewise
+ * constant elements, to name
+ * only one example. Here, the
+ * value on the mother cell has
+ * to be taken the average of the
+ * values on the children,
+ * i.e. all children contribute
+ * alike to the one degree of
+ * freedom. Here, we have to sum
+ * up the contributions of all
+ * child cells with the same
+ * weight, and the non-additive
+ * mode of above would only set
+ * the value on the mother cell
+ * to the value of one of the
+ * child cell, irrespective of
+ * the values on the other cells.
+ *
+ * Similarly, for discontinuous
+ * linear elements, it might be
+ * better to not interpolate the
+ * values at the corners from the
+ * child cells, but to take a
* better average, for example
- * interpolating at the centers of the
- * child cells; in that case, the
- * contributions of the child cells
- * have to be additive as well.
- *
- * Given these notes, the flag under
- * consideration has to be set to #false#
- * for the usual continuous Lagrange
- * elements, and #true# for the other
- * cases mentioned above. The main function
- * where it is used is
+ * interpolating at the centers
+ * of the child cells; in that
+ * case, the contributions of the
+ * child cells have to be
+ * additive as well.
+ *
+ * Given these notes, the flag
+ * under consideration has to be
+ * set to #false# for the usual
+ * continuous Lagrange elements,
+ * and #true# for the other cases
+ * mentioned above. The main
+ * function where it is used is
* #DoFAccessor::get_interpolated_dof_values#.
- * There is one flag per component.
+ * There is one flag per
+ * component.
*/
const vector<bool> restriction_is_additive_flags;
};
/**
- * Finite Element in any dimension. This class declares the functionality
- * to fill the fields of the #FiniteElementBase# class. Since this is
- * something that depends on the actual finite element, the functions are
- * declared virtual if it is not possible to provide a reasonable standard
- * implementation.
+ * Finite Element in any dimension. This class declares the
+ * functionality to fill the fields of the #FiniteElementBase#
+ * class. Since this is something that depends on the actual finite
+ * element, the functions are declared virtual if it is not possible
+ * to provide a reasonable standard implementation.
*
*
* \subsection{Finite elements in one dimension}
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