Fix several simplex quadrature rules.

diff --git a/doc/news/changes/minor/20210622DavidWells b/doc/news/changes/minor/20210622DavidWells
new file mode 100644 (file)
index 0000000..f060eda
--- /dev/null
+++ b/doc/news/changes/minor/20210622DavidWells
@@ -0,0 +1,4 @@
+Fixed: The Gauss-like rules implemented by QGaussSimplex now integrate
+2 * n_points_1D - 1 degree polynomials exactly.
+<br>
+(David Wells, 2021/06/22)

diff --git a/include/deal.II/base/quadrature_lib.h b/include/deal.II/base/quadrature_lib.h
index af9a4c01746f091ad109ef5e2e2b22569264770a..0e17569e45d4acbcbb4237c672f7085e751400b4 100644 (file)
--- a/include/deal.II/base/quadrature_lib.h
+++ b/include/deal.II/base/quadrature_lib.h
@@ -800,13 +800,21 @@ public:
  * QGauss quadrature object, even though the present quadrature formula is not
  * a tensor product. The given value is translated for n_points_1D=1,2,3,4 to
  * following number of quadrature points for 2D and 3D:
- *   - 2D: 1, 3, 7, 15
- *   - 3D: 1, 4, 10, 35
+ * - 2D: 1, 4, 7, 15
+ * - 3D: 1, 6, 14, 35
  *
  * For 1D, the quadrature rule degenerates to a
  * `dealii::QGauss<1>(n_points_1D)`.
  *
  * @ingroup simplex
+ *
+ * @note The quadrature rules implemented by this class come from a variety of
+ * sources, but all of them have positive quadrature weights.
+ *
+ * @note Several of the schemes implemented by this class are not symmetric with
+ * respect to the vertices - i.e., the locations of the mapped quadrature points
+ * depends on the numbering of the cell vertices. If you need rules that are
+ * independent of the vertex numbering then use QWitherdenVincentSimplex.
  */
 template <int dim>
 class QGaussSimplex : public QSimplex<dim>

diff --git a/source/base/quadrature_lib.cc b/source/base/quadrature_lib.cc
index cb755baeb87bfccaf80d7fc876b171755f8ec1f3..083018184c3f42103254d96877c160c09b0b35ff 100644 (file)
--- a/source/base/quadrature_lib.cc
+++ b/source/base/quadrature_lib.cc
@@ -1376,15 +1376,24 @@ QGaussSimplex<dim>::QGaussSimplex(const unsigned int n_points_1D)
         }
       else if (n_points_1D == 2)
         {
-          const double Q23 = 2.0 / 3.0;
-          const double Q16 = 1.0 / 6.0;
-
-          this->quadrature_points.emplace_back(Q23, Q16);
-          this->quadrature_points.emplace_back(Q16, Q23);
-          this->quadrature_points.emplace_back(Q16, Q16);
-          this->weights.emplace_back(Q16);
-          this->weights.emplace_back(Q16);
-          this->weights.emplace_back(Q16);
+          // The Hillion 7 scheme, as communicated by quadpy
+          //
+          // See: Numerical Integration on a Triangle, International Journal for
+          // Numerical Methods in Engineering, 1977
+          const double Q12 = 1.0 / 2.0;
+          this->quadrature_points.emplace_back(0.17855872826361643,
+                                               0.1550510257216822);
+          this->quadrature_points.emplace_back(0.07503111022260812,
+                                               0.6449489742783178);
+          this->quadrature_points.emplace_back(0.6663902460147014,
+                                               0.1550510257216822);
+          this->quadrature_points.emplace_back(0.28001991549907407,
+                                               0.6449489742783178);
+
+          this->weights.emplace_back(0.31804138174397717 * Q12);
+          this->weights.emplace_back(0.18195861825602283 * Q12);
+          this->weights.emplace_back(0.31804138174397717 * Q12);
+          this->weights.emplace_back(0.18195861825602283 * Q12);
         }
       else if (n_points_1D == 3)
         {
@@ -1429,48 +1438,46 @@ QGaussSimplex<dim>::QGaussSimplex(const unsigned int n_points_1D)
           this->quadrature_points.emplace_back(Q14, Q14, Q14);
           this->weights.emplace_back(Q16);
         }
+      // The Xiao Gimbutas 03 scheme, as communicated by quadpy
+      //
+      // See: A numerical algorithm for the construction of efficient quadrature
+      // rules in two and higher dimensions, Computers & Mathematics with
+      // Applications, 2010
       else if (n_points_1D == 2)
         {
-          const double Q124 = 1.0 / 6.0 / 4.0;
-
-          const double palpha = (5.0 + 3.0 * sqrt(5.0)) / 20.0;
-          const double pbeta  = (5.0 - sqrt(5.0)) / 20.0;
-          this->quadrature_points.emplace_back(pbeta, pbeta, pbeta);
-          this->quadrature_points.emplace_back(palpha, pbeta, pbeta);
-          this->quadrature_points.emplace_back(pbeta, palpha, pbeta);
-          this->quadrature_points.emplace_back(pbeta, pbeta, palpha);
-          this->weights.emplace_back(Q124);
-          this->weights.emplace_back(Q124);
-          this->weights.emplace_back(Q124);
-          this->weights.emplace_back(Q124);
+          const double Q16 = 1.0 / 6.0;
+          this->weights.emplace_back(0.1223220027573451 * Q16);
+          this->weights.emplace_back(0.1280664127107469 * Q16);
+          this->weights.emplace_back(0.1325680271444452 * Q16);
+          this->weights.emplace_back(0.1406244096604032 * Q16);
+          this->weights.emplace_back(0.2244151669175574 * Q16);
+          this->weights.emplace_back(0.2520039808095023 * Q16);
+
+          this->quadrature_points.emplace_back(0.1620014916985245,
+                                               0.1838503504920977,
+                                               0.01271836631368145);
+          this->quadrature_points.emplace_back(0.01090521221118924,
+                                               0.2815238021235462,
+                                               0.3621268299455338);
+          this->quadrature_points.emplace_back(0.1901170024392839,
+                                               0.01140332944455717,
+                                               0.3586207204668839);
+          this->quadrature_points.emplace_back(0.170816925164989,
+                                               0.1528181430909273,
+                                               0.6384932999617267);
+          this->quadrature_points.emplace_back(0.1586851632274406,
+                                               0.5856628056552158,
+                                               0.1308471689520965);
+          this->quadrature_points.emplace_back(0.5712260521491151,
+                                               0.1469183900871696,
+                                               0.1403728057942107);
         }
+      // Past this point the best rules (positive weights, minimal number of
+      // points) we have right now are the Witherden-Vincent ones
       else if (n_points_1D == 3)
         {
-          const double Q16 = 1.0 / 6.0;
-
-          // clang-format off
-            this->quadrature_points.emplace_back(0.5684305841968444, 0.1438564719343852, 0.1438564719343852);
-            this->quadrature_points.emplace_back(0.1438564719343852, 0.1438564719343852, 0.1438564719343852);
-            this->quadrature_points.emplace_back(0.1438564719343852, 0.1438564719343852, 0.5684305841968444);
-            this->quadrature_points.emplace_back(0.1438564719343852, 0.5684305841968444, 0.1438564719343852);
-            this->quadrature_points.emplace_back(0.0000000000000000, 0.5000000000000000, 0.5000000000000000);
-            this->quadrature_points.emplace_back(0.5000000000000000, 0.0000000000000000, 0.5000000000000000);
-            this->quadrature_points.emplace_back(0.5000000000000000, 0.5000000000000000, 0.0000000000000000);
-            this->quadrature_points.emplace_back(0.5000000000000000, 0.0000000000000000, 0.0000000000000000);
-            this->quadrature_points.emplace_back(0.0000000000000000, 0.5000000000000000, 0.0000000000000000);
-            this->quadrature_points.emplace_back(0.0000000000000000, 0.0000000000000000, 0.5000000000000000);
-          // clang-format on
-
-          this->weights.emplace_back(0.2177650698804054 * Q16);
-          this->weights.emplace_back(0.2177650698804054 * Q16);
-          this->weights.emplace_back(0.2177650698804054 * Q16);
-          this->weights.emplace_back(0.2177650698804054 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
-          this->weights.emplace_back(0.0214899534130631 * Q16);
+          Quadrature<dim>::operator=(
+            QWitherdenVincentSimplex<dim>(n_points_1D));
         }
       else if (n_points_1D == 4)
         {

diff --git a/tests/simplex/fe_lib_02.output b/tests/simplex/fe_lib_02.output
index cceed5719b6849670eb9a9719ff7a0d2f6752083..ccbb334e422940fe992b09e08d83b6a52f659f12 100644 (file)
--- a/tests/simplex/fe_lib_02.output
+++ b/tests/simplex/fe_lib_02.output
@@ -1,105 +1,133 @@
 
-DEAL:FE_SimplexP<2>(1)::0.666667 0.166667 : 
-DEAL:FE_SimplexP<2>(1)::0.166667 0.666667 0.166667 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
-DEAL:FE_SimplexP<2>(1)::0.166667 0.666667 : 
-DEAL:FE_SimplexP<2>(1)::0.166667 0.166667 0.666667 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
-DEAL:FE_SimplexP<2>(1)::0.166667 0.166667 : 
-DEAL:FE_SimplexP<2>(1)::0.666667 0.166667 0.166667 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<2>(1)::0.178559 0.155051 : 
+DEAL:FE_SimplexP<2>(1)::0.666390 0.178559 0.155051 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<2>(1)::0.0750311 0.644949 : 
+DEAL:FE_SimplexP<2>(1)::0.280020 0.0750311 0.644949 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<2>(1)::0.666390 0.155051 : 
+DEAL:FE_SimplexP<2>(1)::0.178559 0.666390 0.155051 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<2>(1)::0.280020 0.644949 : 
+DEAL:FE_SimplexP<2>(1)::0.0750311 0.280020 0.644949 -1.00000 -1.00000 1.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
 DEAL:FE_SimplexP<2>(1)::
 DEAL:FE_SimplexP<2>(2)::0.333333 0.333333 : 
-DEAL:FE_SimplexP<2>(2)::-0.111111 -0.111111 -0.111111 0.444444 0.444444 0.444444 -0.333333 -0.333333 0.333333 0.00000 0.00000 0.333333 3.99991e-12 -1.33333 1.33333 1.33333 -1.33333 3.99991e-12 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
+DEAL:FE_SimplexP<2>(2)::-0.111111 -0.111111 -0.111111 0.444444 0.444444 0.444444 -0.333333 -0.333333 0.333333 0.00000 0.00000 0.333333 4.44089e-16 -1.33333 1.33333 1.33333 -1.33333 4.44089e-16 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.797427 0.101287 : 
-DEAL:FE_SimplexP<2>(2)::-0.0807686 0.474353 -0.0807686 0.323074 0.323074 0.0410358 0.594854 0.594854 2.18971 0.00000 0.00000 -0.594854 -2.78456 -3.18971 0.405146 3.18971 -0.405146 3.99980e-12 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
+DEAL:FE_SimplexP<2>(2)::-0.0807686 0.474353 -0.0807686 0.323074 0.323074 0.0410358 0.594854 0.594854 2.18971 0.00000 0.00000 -0.594854 -2.78456 -3.18971 0.405146 3.18971 -0.405146 2.22045e-16 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.101287 0.797427 : 
-DEAL:FE_SimplexP<2>(2)::-0.0807686 -0.0807686 0.474353 0.0410358 0.323074 0.323074 0.594854 0.594854 -0.594854 0.00000 0.00000 2.18971 3.99963e-12 -0.405146 3.18971 0.405146 -3.18971 -2.78456 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
+DEAL:FE_SimplexP<2>(2)::-0.0807686 -0.0807686 0.474353 0.0410358 0.323074 0.323074 0.594854 0.594854 -0.594854 0.00000 0.00000 2.18971 1.11022e-16 -0.405146 3.18971 0.405146 -3.18971 -2.78456 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.101287 0.101287 : 
 DEAL:FE_SimplexP<2>(2)::0.474353 -0.0807686 -0.0807686 0.323074 0.0410358 0.323074 -2.18971 -2.18971 -0.594854 0.00000 0.00000 -0.594854 2.78456 -0.405146 0.405146 0.405146 -0.405146 2.78456 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.0597159 0.470142 : 
-DEAL:FE_SimplexP<2>(2)::-0.0280749 -0.0525839 -0.0280749 0.112300 0.112300 0.884134 -0.880568 -0.880568 -0.761137 0.00000 0.00000 0.880568 1.64170 -0.238863 1.88057 0.238863 -1.88057 8.00249e-13 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
+DEAL:FE_SimplexP<2>(2)::-0.0280749 -0.0525839 -0.0280749 0.112300 0.112300 0.884134 -0.880568 -0.880568 -0.761137 0.00000 0.00000 0.880568 1.64170 -0.238863 1.88057 0.238863 -1.88057 4.44089e-16 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.470142 0.0597159 : 
-DEAL:FE_SimplexP<2>(2)::-0.0280749 -0.0280749 -0.0525839 0.884134 0.112300 0.112300 -0.880568 -0.880568 0.880568 0.00000 0.00000 -0.761137 8.00027e-13 -1.88057 0.238863 1.88057 -0.238863 1.64170 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
+DEAL:FE_SimplexP<2>(2)::-0.0280749 -0.0280749 -0.0525839 0.884134 0.112300 0.112300 -0.880568 -0.880568 0.880568 0.00000 0.00000 -0.761137 4.44089e-16 -1.88057 0.238863 1.88057 -0.238863 1.64170 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::0.470142 0.470142 : 
 DEAL:FE_SimplexP<2>(2)::-0.0525839 -0.0280749 -0.0280749 0.112300 0.884134 0.112300 0.761137 0.761137 0.880568 0.00000 0.00000 0.880568 -1.64170 -1.88057 1.88057 1.88057 -1.88057 -1.64170 4.00000 4.00000 4.00000 4.00000 4.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4.00000 -8.00000 -4.00000 -4.00000 0.00000 0.00000 4.00000 4.00000 0.00000 0.00000 -4.00000 -4.00000 -8.00000 
 DEAL:FE_SimplexP<2>(2)::
-DEAL:FE_SimplexP<3>(1)::0.138197 0.138197 0.138197 : 
-DEAL:FE_SimplexP<3>(1)::0.585410 0.138197 0.138197 0.138197 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
-DEAL:FE_SimplexP<3>(1)::0.585410 0.138197 0.138197 : 
-DEAL:FE_SimplexP<3>(1)::0.138197 0.585410 0.138197 0.138197 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
-DEAL:FE_SimplexP<3>(1)::0.138197 0.585410 0.138197 : 
-DEAL:FE_SimplexP<3>(1)::0.138197 0.138197 0.585410 0.138197 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
-DEAL:FE_SimplexP<3>(1)::0.138197 0.138197 0.585410 : 
-DEAL:FE_SimplexP<3>(1)::0.138197 0.138197 0.138197 0.585410 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<3>(1)::0.162001 0.183850 0.0127184 : 
+DEAL:FE_SimplexP<3>(1)::0.641430 0.162001 0.183850 0.0127184 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<3>(1)::0.0109052 0.281524 0.362127 : 
+DEAL:FE_SimplexP<3>(1)::0.345444 0.0109052 0.281524 0.362127 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<3>(1)::0.190117 0.0114033 0.358621 : 
+DEAL:FE_SimplexP<3>(1)::0.439859 0.190117 0.0114033 0.358621 -1.00000 -1.00000 -1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 
+DEAL:FE_SimplexP<3>(1)::0.170817 0.152818 0.638493 : 
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 DEAL:FE_SimplexDGP<3>(2)::

diff --git a/tests/simplex/fe_p_bubbles_02.output b/tests/simplex/fe_p_bubbles_02.output
index 41d0630803db059b8ee08387bceb73b68cf7b047..7b4e8684615d23958a63633caa5b7dff95446bac 100644 (file)
--- a/tests/simplex/fe_p_bubbles_02.output
+++ b/tests/simplex/fe_p_bubbles_02.output
@@ -115,23 +115,23 @@ DEAL::ratio = 1.99086
 DEAL::degree = 1
 DEAL::number of cells = 8
 DEAL::number of dofs = 9
-DEAL::error = 0.112188
+DEAL::error = 0.112372
 DEAL::number of cells = 32
 DEAL::number of dofs = 25
-DEAL::error = 0.0427299
-DEAL::ratio = 2.62551
+DEAL::error = 0.0427498
+DEAL::ratio = 2.62859
 DEAL::number of cells = 128
 DEAL::number of dofs = 81
-DEAL::error = 0.0170503
-DEAL::ratio = 2.50610
+DEAL::error = 0.0170530
+DEAL::ratio = 2.50688
 DEAL::number of cells = 512
 DEAL::number of dofs = 289
-DEAL::error = 0.00659734
-DEAL::ratio = 2.58443
+DEAL::error = 0.00659750
+DEAL::ratio = 2.58476
 DEAL::number of cells = 2048
 DEAL::number of dofs = 1089
-DEAL::error = 0.00268244
-DEAL::ratio = 2.45946
+DEAL::error = 0.00268246
+DEAL::ratio = 2.45950
 DEAL::degree = 2
 DEAL::number of cells = 8
 DEAL::number of dofs = 33
@@ -162,7 +162,7 @@ DEAL::error = 0.110613
 DEAL::number of cells = 192
 DEAL::number of dofs = 192
 DEAL::error = 0.0560060
-DEAL::ratio = 1.97503
+DEAL::ratio = 1.97501
 DEAL::number of cells = 1536
 DEAL::number of dofs = 1536
 DEAL::error = 0.0288177
@@ -174,19 +174,19 @@ DEAL::ratio = 1.98187
 DEAL::degree = 1
 DEAL::number of cells = 24
 DEAL::number of dofs = 14
-DEAL::error = 0.117148
+DEAL::error = 0.117311
 DEAL::number of cells = 192
 DEAL::number of dofs = 63
-DEAL::error = 0.0467977
-DEAL::ratio = 2.50329
+DEAL::error = 0.0468382
+DEAL::ratio = 2.50459
 DEAL::number of cells = 1536
 DEAL::number of dofs = 365
-DEAL::error = 0.0170371
-DEAL::ratio = 2.74682
+DEAL::error = 0.0170426
+DEAL::ratio = 2.74830
 DEAL::number of cells = 12288
 DEAL::number of dofs = 2457
-DEAL::error = 0.00632181
-DEAL::ratio = 2.69496
+DEAL::error = 0.00632241
+DEAL::ratio = 2.69559
 DEAL::degree = 2
 DEAL::number of cells = 24
 DEAL::number of dofs = 147

diff --git a/tests/simplex/matrix_free_01.output b/tests/simplex/matrix_free_01.output
index 83ee05c055cde84d0cea4d86dedecccc50d07d2f..01b448a0a6357ae56a3ddd46543acc370cd52dc1 100644 (file)
--- a/tests/simplex/matrix_free_01.output
+++ b/tests/simplex/matrix_free_01.output
@@ -6,7 +6,7 @@ DEAL:SIMPLEX::dim=2 degree=2 Type=Helmholtz : Convergence step 36 value 0.000294
 DEAL:SIMPLEX::dim=3 degree=1 Type=Possion   : Convergence step 7 value 0.000281643.
 DEAL:SIMPLEX::dim=3 degree=1 Type=Helmholtz : Convergence step 7 value 0.000268188.
 DEAL:SIMPLEX::dim=3 degree=2 Type=Possion   : Convergence step 20 value 0.000146315.
-DEAL:SIMPLEX::dim=3 degree=2 Type=Helmholtz : Convergence step 20 value 0.000137731.
+DEAL:SIMPLEX::dim=3 degree=2 Type=Helmholtz : Convergence step 20 value 0.000137758.
 DEAL:WEDGE  ::dim=3 degree=1 Type=Possion   : Convergence step 7 value 0.000224296.
 DEAL:WEDGE  ::dim=3 degree=1 Type=Helmholtz : Convergence step 7 value 0.000211401.
 DEAL:WEDGE  ::dim=3 degree=2 Type=Possion   : Convergence step 20 value 0.000133408.

diff --git a/tests/simplex/matrix_free_03.output b/tests/simplex/matrix_free_03.output
index 730828db408acd1e035bf1b807a0c61f0daa10c5..e2a2ab6c30da17139b251e2c7c7298031f403cc7 100644 (file)
--- a/tests/simplex/matrix_free_03.output
+++ b/tests/simplex/matrix_free_03.output
@@ -5,5 +5,5 @@ DEAL::dim=2 degree=2 0.0412685
 DEAL::dim=2 degree=2 0.0412685
 DEAL::dim=3 degree=1 0.0258555
 DEAL::dim=3 degree=1 0.0258555
-DEAL::dim=3 degree=2 0.0250053
-DEAL::dim=3 degree=2 0.0250053
+DEAL::dim=3 degree=2 0.0250341
+DEAL::dim=3 degree=2 0.0250342

diff --git a/tests/simplex/poisson_02.output b/tests/simplex/poisson_02.output
index 825396daad5cf3d3b3b7c58b1857b37b8f53342d..ffb2f84e9cde216ee6e12a9cb921c3253b343e10 100644 (file)
--- a/tests/simplex/poisson_02.output
+++ b/tests/simplex/poisson_02.output
@@ -1,8 +1,8 @@
 
      error      cells    dofs    
-3.0924e-01 -    32    96   -     
-1.1363e-01 1.44 128   384  -2.00 
-3.2531e-02 1.80 512   1536 -2.00 
+3.2011e-01 -    32    96   -     
+1.1594e-01 1.47 128   384  -2.00 
+3.3058e-02 1.81 512   1536 -2.00 
 DEAL::
      error      cells    dofs    
 3.2745e-02 -    32    192  -     
@@ -10,12 +10,12 @@ DEAL::
 4.1566e-04 3.12 512   3072 -2.00 
 DEAL::
      error      cells    dofs     
-1.6346e-01 -    320   1280  -     
-1.0816e-01 0.60 2560  10240 -3.00 
+1.7408e-01 -    320   1280  -     
+1.1438e-01 0.61 2560  10240 -3.00 
 DEAL::
      error      cells    dofs     
-8.4685e-02 -    320   3200  -     
-9.4765e-03 3.16 2560  25600 -3.00 
+6.4411e-02 -    320   3200  -     
+6.4074e-03 3.33 2560  25600 -3.00 
 DEAL::
      error      cells    dofs    
 1.6226e-01 -    16    64   -     

diff --git a/tests/simplex/q_projection_01.output b/tests/simplex/q_projection_01.output
index ed748deec4c6da3cd95790ced794a1d0976e597f..d6e0e3a2b0161f0781222f4e3986cd6c021f7a8d 100644 (file)
--- a/tests/simplex/q_projection_01.output
+++ b/tests/simplex/q_projection_01.output
@@ -144,124 +144,148 @@ DEAL:3d-1::face_no=3 face_orientation=false face_flip=false face_rotation=true:
 DEAL:3d-1::0.333333 0.333333 0.333333 0.866025 
 DEAL:3d-1::
 DEAL:3d-4::face_no=0 face_orientation=true face_flip=false face_rotation=false:
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
+DEAL:3d-4::0.178559 0.155051 0.00000 0.159021 
+DEAL:3d-4::0.0750311 0.644949 0.00000 0.0909793 
+DEAL:3d-4::0.666390 0.155051 0.00000 0.159021 
+DEAL:3d-4::0.280020 0.644949 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=0 face_orientation=true face_flip=true face_rotation=false:
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
+DEAL:3d-4::0.155051 0.666390 0.00000 0.159021 
+DEAL:3d-4::0.644949 0.280020 0.00000 0.0909793 
+DEAL:3d-4::0.155051 0.178559 0.00000 0.159021 
+DEAL:3d-4::0.644949 0.0750311 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=0 face_orientation=true face_flip=false face_rotation=true:
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
+DEAL:3d-4::0.666390 0.178559 0.00000 0.159021 
+DEAL:3d-4::0.280020 0.0750311 0.00000 0.0909793 
+DEAL:3d-4::0.178559 0.666390 0.00000 0.159021 
+DEAL:3d-4::0.0750311 0.280020 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=0 face_orientation=false face_flip=false face_rotation=false:
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
+DEAL:3d-4::0.155051 0.178559 0.00000 0.159021 
+DEAL:3d-4::0.644949 0.0750311 0.00000 0.0909793 
+DEAL:3d-4::0.155051 0.666390 0.00000 0.159021 
+DEAL:3d-4::0.644949 0.280020 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=0 face_orientation=false face_flip=true face_rotation=false:
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
+DEAL:3d-4::0.666390 0.155051 0.00000 0.159021 
+DEAL:3d-4::0.280020 0.644949 0.00000 0.0909793 
+DEAL:3d-4::0.178559 0.155051 0.00000 0.159021 
+DEAL:3d-4::0.0750311 0.644949 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=0 face_orientation=false face_flip=false face_rotation=true:
-DEAL:3d-4::0.666667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.166667 0.00000 0.166667 
-DEAL:3d-4::0.166667 0.666667 0.00000 0.166667 
+DEAL:3d-4::0.178559 0.666390 0.00000 0.159021 
+DEAL:3d-4::0.0750311 0.280020 0.00000 0.0909793 
+DEAL:3d-4::0.666390 0.178559 0.00000 0.159021 
+DEAL:3d-4::0.280020 0.0750311 0.00000 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=true face_flip=false face_rotation=false:
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
+DEAL:3d-4::0.666390 0.00000 0.155051 0.159021 
+DEAL:3d-4::0.280020 0.00000 0.644949 0.0909793 
+DEAL:3d-4::0.178559 0.00000 0.155051 0.159021 
+DEAL:3d-4::0.0750311 0.00000 0.644949 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=true face_flip=true face_rotation=false:
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
+DEAL:3d-4::0.178559 0.00000 0.666390 0.159021 
+DEAL:3d-4::0.0750311 0.00000 0.280020 0.0909793 
+DEAL:3d-4::0.666390 0.00000 0.178559 0.159021 
+DEAL:3d-4::0.280020 0.00000 0.0750311 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=true face_flip=false face_rotation=true:
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
+DEAL:3d-4::0.155051 0.00000 0.178559 0.159021 
+DEAL:3d-4::0.644949 0.00000 0.0750311 0.0909793 
+DEAL:3d-4::0.155051 0.00000 0.666390 0.159021 
+DEAL:3d-4::0.644949 0.00000 0.280020 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=false face_flip=false face_rotation=false:
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
+DEAL:3d-4::0.666390 0.00000 0.178559 0.159021 
+DEAL:3d-4::0.280020 0.00000 0.0750311 0.0909793 
+DEAL:3d-4::0.178559 0.00000 0.666390 0.159021 
+DEAL:3d-4::0.0750311 0.00000 0.280020 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=false face_flip=true face_rotation=false:
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
+DEAL:3d-4::0.178559 0.00000 0.155051 0.159021 
+DEAL:3d-4::0.0750311 0.00000 0.644949 0.0909793 
+DEAL:3d-4::0.666390 0.00000 0.155051 0.159021 
+DEAL:3d-4::0.280020 0.00000 0.644949 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=1 face_orientation=false face_flip=false face_rotation=true:
-DEAL:3d-4::0.166667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.666667 0.00000 0.166667 0.166667 
-DEAL:3d-4::0.166667 0.00000 0.666667 0.166667 
+DEAL:3d-4::0.155051 0.00000 0.666390 0.159021 
+DEAL:3d-4::0.644949 0.00000 0.280020 0.0909793 
+DEAL:3d-4::0.155051 0.00000 0.178559 0.159021 
+DEAL:3d-4::0.644949 0.00000 0.0750311 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=true face_flip=false face_rotation=false:
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
+DEAL:3d-4::0.00000 0.178559 0.155051 0.159021 
+DEAL:3d-4::0.00000 0.0750311 0.644949 0.0909793 
+DEAL:3d-4::0.00000 0.666390 0.155051 0.159021 
+DEAL:3d-4::0.00000 0.280020 0.644949 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=true face_flip=true face_rotation=false:
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
+DEAL:3d-4::0.00000 0.155051 0.666390 0.159021 
+DEAL:3d-4::0.00000 0.644949 0.280020 0.0909793 
+DEAL:3d-4::0.00000 0.155051 0.178559 0.159021 
+DEAL:3d-4::0.00000 0.644949 0.0750311 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=true face_flip=false face_rotation=true:
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
+DEAL:3d-4::0.00000 0.666390 0.178559 0.159021 
+DEAL:3d-4::0.00000 0.280020 0.0750311 0.0909793 
+DEAL:3d-4::0.00000 0.178559 0.666390 0.159021 
+DEAL:3d-4::0.00000 0.0750311 0.280020 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=false face_flip=false face_rotation=false:
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
+DEAL:3d-4::0.00000 0.155051 0.178559 0.159021 
+DEAL:3d-4::0.00000 0.644949 0.0750311 0.0909793 
+DEAL:3d-4::0.00000 0.155051 0.666390 0.159021 
+DEAL:3d-4::0.00000 0.644949 0.280020 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=false face_flip=true face_rotation=false:
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
+DEAL:3d-4::0.00000 0.666390 0.155051 0.159021 
+DEAL:3d-4::0.00000 0.280020 0.644949 0.0909793 
+DEAL:3d-4::0.00000 0.178559 0.155051 0.159021 
+DEAL:3d-4::0.00000 0.0750311 0.644949 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=2 face_orientation=false face_flip=false face_rotation=true:
-DEAL:3d-4::0.00000 0.666667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.166667 0.166667 
-DEAL:3d-4::0.00000 0.166667 0.666667 0.166667 
+DEAL:3d-4::0.00000 0.178559 0.666390 0.159021 
+DEAL:3d-4::0.00000 0.0750311 0.280020 0.0909793 
+DEAL:3d-4::0.00000 0.666390 0.178559 0.159021 
+DEAL:3d-4::0.00000 0.280020 0.0750311 0.0909793 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=true face_flip=false face_rotation=false:
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
+DEAL:3d-4::0.178559 0.666390 0.155051 0.275432 
+DEAL:3d-4::0.0750311 0.280020 0.644949 0.157581 
+DEAL:3d-4::0.666390 0.178559 0.155051 0.275432 
+DEAL:3d-4::0.280020 0.0750311 0.644949 0.157581 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=true face_flip=true face_rotation=false:
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
+DEAL:3d-4::0.155051 0.178559 0.666390 0.275432 
+DEAL:3d-4::0.644949 0.0750311 0.280020 0.157581 
+DEAL:3d-4::0.155051 0.666390 0.178559 0.275432 
+DEAL:3d-4::0.644949 0.280020 0.0750311 0.157581 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=true face_flip=false face_rotation=true:
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
+DEAL:3d-4::0.666390 0.155051 0.178559 0.275432 
+DEAL:3d-4::0.280020 0.644949 0.0750311 0.157581 
+DEAL:3d-4::0.178559 0.155051 0.666390 0.275432 
+DEAL:3d-4::0.0750311 0.644949 0.280020 0.157581 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=false face_flip=false face_rotation=false:
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
+DEAL:3d-4::0.155051 0.666390 0.178559 0.275432 
+DEAL:3d-4::0.644949 0.280020 0.0750311 0.157581 
+DEAL:3d-4::0.155051 0.178559 0.666390 0.275432 
+DEAL:3d-4::0.644949 0.0750311 0.280020 0.157581 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=false face_flip=true face_rotation=false:
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
+DEAL:3d-4::0.666390 0.178559 0.155051 0.275432 
+DEAL:3d-4::0.280020 0.0750311 0.644949 0.157581 
+DEAL:3d-4::0.178559 0.666390 0.155051 0.275432 
+DEAL:3d-4::0.0750311 0.280020 0.644949 0.157581 
 DEAL:3d-4::
 DEAL:3d-4::face_no=3 face_orientation=false face_flip=false face_rotation=true:
-DEAL:3d-4::0.666667 0.166667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.666667 0.166667 0.288675 
-DEAL:3d-4::0.166667 0.166667 0.666667 0.288675 
+DEAL:3d-4::0.178559 0.155051 0.666390 0.275432 
+DEAL:3d-4::0.0750311 0.644949 0.280020 0.157581 
+DEAL:3d-4::0.666390 0.155051 0.178559 0.275432 
+DEAL:3d-4::0.280020 0.644949 0.0750311 0.157581 
 DEAL:3d-4::
 DEAL:3d-10::face_no=0 face_orientation=true face_flip=false face_rotation=false:
 DEAL:3d-10::0.333333 0.333333 0.00000 0.112500 

diff --git a/tests/simplex/qgauss_01.output b/tests/simplex/qgauss_01.output
index d69117871d2f220e8501a051190e0fa14f8a0790..005640a101254ccdd319a42d2a3aaf5742a51130 100644 (file)
--- a/tests/simplex/qgauss_01.output
+++ b/tests/simplex/qgauss_01.output
@@ -4,7 +4,7 @@ DEAL::
 DEAL::Monomial powers = 0.00000 1.00000
 DEAL::Integrand = 0.1666666666666667
 DEAL::Monomial powers = 1.00000 2.00000
-DEAL::Integrand = 0.01620370370370370
+DEAL::Integrand = 0.01666666666666667
 DEAL::Monomial powers = 2.00000 3.00000
 DEAL::Integrand = 0.002380952380952380
 DEAL::Monomial powers = 3.00000 4.00000
@@ -12,8 +12,8 @@ DEAL::Integrand = 0.0003968253968253969
 DEAL::Monomial powers = 0.00000 0.00000 1.00000
 DEAL::Integrand = 0.04166666666666666
 DEAL::Monomial powers = 1.00000 1.00000 1.00000
-DEAL::Integrand = 0.001507514161979123
+DEAL::Integrand = 0.001388888888888889
 DEAL::Monomial powers = 1.00000 1.00000 3.00000
-DEAL::Integrand = 0.0001578591272523996
+DEAL::Integrand = 0.0001488095238095239
 DEAL::Monomial powers = 2.00000 2.00000 3.00000
 DEAL::Integrand = 6.613756613756609e-06

diff --git a/tests/simplex/quadrature_lib_01.output b/tests/simplex/quadrature_lib_01.output
index d2a4bff8c8c17fb0b354322a8c77dedbd76764cf..917f2f520c73854df3c305ecb22b4f0ae34735fd 100644 (file)
--- a/tests/simplex/quadrature_lib_01.output
+++ b/tests/simplex/quadrature_lib_01.output
@@ -5,10 +5,11 @@ DEAL:1d-2::0.788675 0.500000
 DEAL:1d-3::0.112702 0.277778 
 DEAL:1d-3::0.500000 0.444444 
 DEAL:1d-3::0.887298 0.277778 
-DEAL:2d-1::0.333333 0.333333 0.50000 
-DEAL:2d-3::0.666667 0.166667 0.166667 
-DEAL:2d-3::0.166667 0.666667 0.166667 
-DEAL:2d-3::0.166667 0.166667 0.166667 
+DEAL:2d-1::0.333333 0.333333 0.500000 
+DEAL:2d-3::0.178559 0.155051 0.159021 
+DEAL:2d-3::0.0750311 0.644949 0.0909793 
+DEAL:2d-3::0.666390 0.155051 0.159021 
+DEAL:2d-3::0.280020 0.644949 0.0909793 
 DEAL:2d-7::0.333333 0.333333 0.112500 
 DEAL:2d-7::0.797427 0.101287 0.0629696 
 DEAL:2d-7::0.101287 0.797427 0.0629696 
@@ -17,17 +18,23 @@ DEAL:2d-7::0.0597159 0.470142 0.0661971
 DEAL:2d-7::0.470142 0.0597159 0.0661971 
 DEAL:2d-7::0.470142 0.470142 0.0661971 
 DEAL:3d-1::0.250000 0.250000 0.250000 0.166667 
-DEAL:3d-4::0.138197 0.138197 0.138197 0.0416667 
-DEAL:3d-4::0.585410 0.138197 0.138197 0.0416667 
-DEAL:3d-4::0.138197 0.585410 0.138197 0.0416667 
-DEAL:3d-4::0.138197 0.138197 0.585410 0.0416667 
-DEAL:3d-10::0.568431 0.143856 0.143856 0.0362942 
-DEAL:3d-10::0.143856 0.143856 0.143856 0.0362942 
-DEAL:3d-10::0.143856 0.143856 0.568431 0.0362942 
-DEAL:3d-10::0.143856 0.568431 0.143856 0.0362942 
-DEAL:3d-10::0.00000 0.500000 0.500000 0.00358166 
-DEAL:3d-10::0.500000 0.00000 0.500000 0.00358166 
-DEAL:3d-10::0.500000 0.500000 0.00000 0.00358166 
-DEAL:3d-10::0.500000 0.00000 0.00000 0.00358166 
-DEAL:3d-10::0.00000 0.500000 0.00000 0.00358166 
-DEAL:3d-10::0.00000 0.00000 0.500000 0.00358166 
+DEAL:3d-4::0.162001 0.183850 0.0127184 0.0203870 
+DEAL:3d-4::0.0109052 0.281524 0.362127 0.0213444 
+DEAL:3d-4::0.190117 0.0114033 0.358621 0.0220947 
+DEAL:3d-4::0.170817 0.152818 0.638493 0.0234374 
+DEAL:3d-4::0.158685 0.585663 0.130847 0.0374025 
+DEAL:3d-4::0.571226 0.146918 0.140373 0.0420007 
+DEAL:3d-10::0.0673422 0.310886 0.310886 0.0187813 
+DEAL:3d-10::0.310886 0.0673422 0.310886 0.0187813 
+DEAL:3d-10::0.310886 0.310886 0.0673422 0.0187813 
+DEAL:3d-10::0.310886 0.310886 0.310886 0.0187813 
+DEAL:3d-10::0.0927353 0.0927353 0.0927353 0.0122488 
+DEAL:3d-10::0.0927353 0.0927353 0.721794 0.0122488 
+DEAL:3d-10::0.0927353 0.721794 0.0927353 0.0122488 
+DEAL:3d-10::0.721794 0.0927353 0.0927353 0.0122488 
+DEAL:3d-10::0.0455037 0.0455037 0.454496 0.00709100 
+DEAL:3d-10::0.0455037 0.454496 0.0455037 0.00709100 
+DEAL:3d-10::0.0455037 0.454496 0.454496 0.00709100 
+DEAL:3d-10::0.454496 0.0455037 0.0455037 0.00709100 
+DEAL:3d-10::0.454496 0.0455037 0.454496 0.00709100 
+DEAL:3d-10::0.454496 0.454496 0.0455037 0.00709100 

diff --git a/tests/simplex/step-04.output b/tests/simplex/step-04.output
index f1a975bbd9bd53d3c8f7ed412e680098b50c8ed7..2b996f6d870494635cb3572ae524f057f5a20da3 100644 (file)
--- a/tests/simplex/step-04.output
+++ b/tests/simplex/step-04.output
@@ -4,12 +4,12 @@ DEAL::   Number of active cells: 512
 DEAL::   Total number of cells: 512
 DEAL::   Number of degrees of freedom: 289
 DEAL:cg::Starting value 11.6837
-DEAL:cg::Convergence step 33 value 2.19749e-16
+DEAL:cg::Convergence step 33 value 6.23059e-17
 DEAL::   33 CG iterations needed to obtain convergence.
 DEAL::Solving problem in 3 space dimensions.
 DEAL::   Number of active cells: 12288
 DEAL::   Total number of cells: 12288
 DEAL::   Number of degrees of freedom: 2457
-DEAL:cg::Starting value 13.9290
-DEAL:cg::Convergence step 46 value 8.50319e-13
-DEAL::   46 CG iterations needed to obtain convergence.
+DEAL:cg::Starting value 13.9291
+DEAL:cg::Convergence step 50 value 5.74165e-13
+DEAL::   50 CG iterations needed to obtain convergence.

diff --git a/tests/simplex/step-07.output b/tests/simplex/step-07.output
index 4fe8ec18c4c32afb920a926beaaf126c03820ca4..8ac8c0b0fd69a8af50005394b3c41be56bb043ad 100644 (file)
--- a/tests/simplex/step-07.output
+++ b/tests/simplex/step-07.output
@@ -6,25 +6,25 @@ DEAL::
 DEAL::Solving with P1 elements, global refinement
 DEAL::===========================================
 DEAL::
-DEAL:cg::Starting value 4.36155
-DEAL:cg::Convergence step 32 value 4.41596e-13
+DEAL:cg::Starting value 4.31042
+DEAL:cg::Convergence step 32 value 4.40009e-13
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       512
 DEAL::   Number of degrees of freedom: 289
-DEAL:cg::Starting value 2.73911
-DEAL:cg::Convergence step 58 value 8.84507e-13
+DEAL:cg::Starting value 2.73770
+DEAL:cg::Convergence step 58 value 8.84330e-13
 DEAL::Cycle 1:
 DEAL::   Number of active cells:       2048
 DEAL::   Number of degrees of freedom: 1089
-DEAL:cg::Starting value 1.49437
-DEAL:cg::Convergence step 113 value 6.96045e-13
+DEAL:cg::Starting value 1.49432
+DEAL:cg::Convergence step 113 value 6.96029e-13
 DEAL::Cycle 2:
 DEAL::   Number of active cells:       8192
 DEAL::   Number of degrees of freedom: 4225
 DEAL::
 cycle cells dofs    L2        H1      Linfty   
-0     512   289  1.342e-01 3.074e+00 8.185e-01 
-1     2048  1089 4.203e-02 1.878e+00 3.749e-01 
+0     512   289  1.335e-01 3.062e+00 8.074e-01 
+1     2048  1089 4.205e-02 1.878e+00 3.744e-01 
 2     8192  4225 1.131e-02 9.927e-01 1.125e-01 
 \documentclass[10pt]{report}
 \usepackage{float}
@@ -35,8 +35,8 @@ cycle cells dofs    L2        H1      Linfty
 \begin{center}
 \begin{tabular}{|c|r|r|c|c|c|} \hline
 cycle & \# cells & \# dofs & $L^2$-error & $H^1$-error & $L^\infty$-error\\ \hline
-0 & 512 & 289 & 1.342e-01 & 3.074e+00 & 8.185e-01\\ \hline
-1 & 2048 & 1089 & 4.203e-02 & 1.878e+00 & 3.749e-01\\ \hline
+0 & 512 & 289 & 1.335e-01 & 3.062e+00 & 8.074e-01\\ \hline
+1 & 2048 & 1089 & 4.205e-02 & 1.878e+00 & 3.744e-01\\ \hline
 2 & 8192 & 4225 & 1.131e-02 & 9.927e-01 & 1.125e-01\\ \hline
 \end{tabular}
 \end{center}
@@ -44,8 +44,8 @@ cycle & \# cells & \# dofs & $L^2$-error & $H^1$-error & $L^\infty$-error\\ \hli
 \end{document}
 DEAL::
 n cells         H1                  L2          
-0 512   3.074e+00 -    -    1.342e-01 -    -    
-1 2048  1.878e+00 1.64 0.71 4.203e-02 3.19 1.68 
+0 512   3.062e+00 -    -    1.335e-01 -    -    
+1 2048  1.878e+00 1.63 0.71 4.205e-02 3.17 1.67 
 2 8192  9.927e-01 1.89 0.92 1.131e-02 3.72 1.89 
 DEAL::
 DEAL::Solving with P2 elements, global refinement

diff --git a/tests/simplex/step-12.output b/tests/simplex/step-12.output
index f6149cf94475aab37b29bbdd0037e6cbf7b5a980..69c23db213a7d94ab78adec61dbd4286adaffe1e 100644 (file)
--- a/tests/simplex/step-12.output
+++ b/tests/simplex/step-12.output
@@ -3,22 +3,22 @@ Cycle 0
   Number of degrees of freedom: 24
   Solver converged in 7 iterations.
   Writing solution to <solution-0.vtk>
-  L-infinity norm: 1.00799
+  L-infinity norm: 0.993328
 Cycle 1
   Number of active cells:       32
   Number of degrees of freedom: 96
-  Solver converged in 8 iterations.
+  Solver converged in 7 iterations.
   Writing solution to <solution-1.vtk>
-  L-infinity norm: 1.14371
+  L-infinity norm: 1.14625
 Cycle 2
   Number of active cells:       128
   Number of degrees of freedom: 384
   Solver converged in 11 iterations.
   Writing solution to <solution-2.vtk>
-  L-infinity norm: 1.09928
+  L-infinity norm: 1.10592
 Cycle 3
   Number of active cells:       512
   Number of degrees of freedom: 1536
   Solver converged in 21 iterations.
   Writing solution to <solution-3.vtk>
-  L-infinity norm: 1.11521
+  L-infinity norm: 1.11957

diff --git a/tests/simplex/step-12a.output b/tests/simplex/step-12a.output
index 7fbe5eb0f73c1d1509cc6a9351f22300b593e771..60ec7a06375d7b76ef5d95acb1e9c90ca006a174 100644 (file)
--- a/tests/simplex/step-12a.output
+++ b/tests/simplex/step-12a.output
@@ -3,13 +3,13 @@ DEAL::Cycle 0
 DEAL::  Number of active cells:       2048
 DEAL::  Number of degrees of freedom: 12288
 DEAL:Richardson::Starting value 0.0883883
-DEAL:Richardson::Convergence step 16 value 9.71637e-17
+DEAL:Richardson::Convergence step 16 value 8.69225e-17
 DEAL::  Solver converged in 16 iterations.
 DEAL::  L-infinity norm: 2.33280
 DEAL::Cycle 0
 DEAL::  Number of active cells:       2560
 DEAL::  Number of degrees of freedom: 25600
 DEAL:Richardson::Starting value 0.0360844
-DEAL:Richardson::Convergence step 13 value 2.52800e-14
+DEAL:Richardson::Convergence step 13 value 1.78265e-14
 DEAL::  Solver converged in 13 iterations.
-DEAL::  L-infinity norm: 13.9260
+DEAL::  L-infinity norm: 14.2242

diff --git a/tests/simplex/step-12b.output b/tests/simplex/step-12b.output
index 89ed3cd545ee7657141d687626f265fa0cb0a445..265e33a1816325f75574fc9d11553d03b2d59db8 100644 (file)
--- a/tests/simplex/step-12b.output
+++ b/tests/simplex/step-12b.output
@@ -3,9 +3,9 @@ DEAL::Cycle 0:
 DEAL::   Number of active cells:       512
 DEAL::   Number of degrees of freedom: 1536
 DEAL::  0.125000
-DEAL::  17.2926
+DEAL::  17.2949
 DEAL::  0.125000
-DEAL::  17.2926
+DEAL::  17.2949
 DEAL::solution1 and solution2 coincide.
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       512
@@ -35,33 +35,33 @@ DEAL::Cycle 0:
 DEAL::   Number of active cells:       2560
 DEAL::   Number of degrees of freedom: 10240
 DEAL::  0.0360844
-DEAL::  45.1474
+DEAL::  45.1833
 DEAL::  0.0360844
-DEAL::  45.1474
+DEAL::  45.1833
 DEAL::solution1 and solution2 coincide.
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       2560
 DEAL::   Number of degrees of freedom: 25600
 DEAL::  0.0360844
-DEAL::  69.8629
+DEAL::  69.8864
 DEAL::  0.0360844
-DEAL::  69.8629
+DEAL::  69.8864
 DEAL::solution1 and solution2 coincide.
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       3072
 DEAL::   Number of degrees of freedom: 15360
 DEAL::  0.0441942
-DEAL::  54.8297
+DEAL::  54.8271
 DEAL::  0.0441942
-DEAL::  54.8297
+DEAL::  54.8271
 DEAL::solution1 and solution2 coincide.
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       1024
 DEAL::   Number of degrees of freedom: 6144
 DEAL::  0.0441942
-DEAL::  34.6857
+DEAL::  34.7035
 DEAL::  0.0441942
-DEAL::  34.6857
+DEAL::  34.7035
 DEAL::solution1 and solution2 coincide.
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       1024

diff --git a/tests/simplex/step-12c.output b/tests/simplex/step-12c.output
index b8e96aab025842f2c11e07029145ba57dfa1db51..a0a1352339ea175c42d91458f87e78b050dcbde2 100644 (file)
--- a/tests/simplex/step-12c.output
+++ b/tests/simplex/step-12c.output
@@ -3,7 +3,7 @@ DEAL::Cycle 0:
 DEAL::   Number of active cells:       512
 DEAL::   Number of degrees of freedom: 1536
 DEAL::  0.125000
-DEAL::  17.2926
+DEAL::  17.2949
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       512
 DEAL::   Number of degrees of freedom: 3072
@@ -23,22 +23,22 @@ DEAL::Cycle 0:
 DEAL::   Number of active cells:       2560
 DEAL::   Number of degrees of freedom: 10240
 DEAL::  0.0360844
-DEAL::  45.1474
+DEAL::  45.1833
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       2560
 DEAL::   Number of degrees of freedom: 25600
 DEAL::  0.0360844
-DEAL::  69.8629
+DEAL::  69.8864
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       3072
 DEAL::   Number of degrees of freedom: 15360
 DEAL::  0.0441942
-DEAL::  54.8297
+DEAL::  54.8271
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       1024
 DEAL::   Number of degrees of freedom: 6144
 DEAL::  0.0441942
-DEAL::  34.6857
+DEAL::  34.7035
 DEAL::Cycle 0:
 DEAL::   Number of active cells:       1024
 DEAL::   Number of degrees of freedom: 18432

diff --git a/tests/simplex/variable_face_quadratures_03.output b/tests/simplex/variable_face_quadratures_03.output
index c8b88bfefdbaff49d8e90f8be0d32c6ae453f7d1..6b1ea947d5d9ce640cc8945fd6d37d3ab61bc720 100644 (file)
--- a/tests/simplex/variable_face_quadratures_03.output
+++ b/tests/simplex/variable_face_quadratures_03.output
@@ -15,9 +15,10 @@ DEAL:dim=3::face_no=0:
 DEAL:dim=3::0.333333 0.333333  0.00000 
 DEAL:dim=3::
 DEAL:dim=3::face_no=1:
-DEAL:dim=3::0.166667 0.00000  0.166667 
-DEAL:dim=3::0.166667 0.00000  0.666667 
-DEAL:dim=3::0.666667 0.00000  0.166667 
+DEAL:dim=3::0.666390 0.00000  0.155051 
+DEAL:dim=3::0.280020 0.00000  0.644949 
+DEAL:dim=3::0.178559 0.00000  0.155051 
+DEAL:dim=3::0.0750311 0.00000  0.644949 
 DEAL:dim=3::
 DEAL:dim=3::face_no=2:
 DEAL:dim=3::0.00000 0.333333  0.333333