From b2e97311b0fbb11e95fc755c581572308af835ea Mon Sep 17 00:00:00 2001
From: Wolfgang Bangerth <bangerth@colostate.edu>
Date: Thu, 5 May 2022 14:59:41 -0600
Subject: [PATCH] Provide ReferenceCell::get_midpoint_quadrature().

---
 include/deal.II/grid/reference_cell.h | 31 +++++++++++++++++++++++----
 1 file changed, 27 insertions(+), 4 deletions(-)

diff --git a/include/deal.II/grid/reference_cell.h b/include/deal.II/grid/reference_cell.h
index 5431a59092..1a6ec8f8de 100644
--- a/include/deal.II/grid/reference_cell.h
+++ b/include/deal.II/grid/reference_cell.h
@@ -204,10 +204,23 @@ public:
   get_gauss_type_quadrature(const unsigned n_points_1D) const;
 
   /**
-   * Return a quadrature rule with the support points of the given reference
-   * cell. For 1d line segments, this corresponds to the quadrature points
-   * of the trapezoidal rule, which by taking tensor products easily
-   * generalizes also to other hypercube elements (see also QTrapezoid).
+   * Return a quadrature object that has a single quadrature point at the
+   * barycenter of the cell with quadrature weight equal to the volume of the
+   * reference cell. This quadrature formula is exact for integrals of constant
+   * and linear integrands.
+   *
+   * The object returned by this function generalizes what the QMidpoint class
+   * represents to other reference cells.
+   */
+  template <int dim>
+  Quadrature<dim>
+  get_midpoint_quadrature() const;
+
+  /**
+   * Return a quadrature rule whose quadrature points are the vertices of the
+   * given reference cell. For 1d line segments, this corresponds to the
+   * quadrature points of the trapezoidal rule, which by taking tensor products
+   * easily generalizes also to other hypercube elements (see also QTrapezoid).
    * For all reference cell shapes, the quadrature points are ordered
    * in the same order as the vertices of the reference cell.
    *
@@ -926,6 +939,16 @@ ReferenceCell::get_dimension() const
 
 
 
+template <int dim>
+Quadrature<dim>
+ReferenceCell::get_midpoint_quadrature() const
+{
+  return Quadrature<dim>(std::vector<Point<dim>>({barycenter<dim>()}),
+                         std::vector<double>({volume()}));
+}
+
+
+
 inline unsigned int
 ReferenceCell::n_vertices() const
 {
-- 
2.39.5