]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Choose different weights for the new point on a quad and in the
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Fri, 2 Mar 2001 09:54:59 +0000 (09:54 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Fri, 2 Mar 2001 09:54:59 +0000 (09:54 +0000)
interior of a hex.

git-svn-id: https://svn.dealii.org/trunk@4088 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/deal.II/source/grid/tria.cc
deal.II/doc/news/2001/c-3-1.html
tests/deal.II/grid_test.checked

index cfe83ed5b68fa9a018778a27efa2071a1d9cc5ca..1140817c4b3362d58b66eff9504793607c470245 100644 (file)
@@ -4869,9 +4869,10 @@ void Triangulation<3>::execute_refinement ()
                                               // the mean value of
                                               // the 4 vertices of
                                               // the face, but rather
-                                              // as the mean value of
-                                              // the 8 vertices which
-                                              // we already have (the
+                                              // as a weighted mean
+                                              // value of the 8
+                                              // vertices which we
+                                              // already have (the
                                               // four old ones, and
                                               // the four ones
                                               // inserted as middle
@@ -4883,13 +4884,26 @@ void Triangulation<3>::execute_refinement ()
                                               // whether one of the
                                               // lines is at the
                                               // boundary
+                                              //
+                                              // note that the exact
+                                              // weights are chosen
+                                              // such as to minimize
+                                              // the distortion of
+                                              // the four new quads
+                                              // from the optimal
+                                              // shape; their
+                                              // derivation and
+                                              // values is copied
+                                              // over from the
+                                              // @p{MappingQ::set_laplace_on_vector}
+                                              // function
              vertices[next_unused_vertex]
                = (quad->vertex(0) + quad->vertex(1) +
                   quad->vertex(2) + quad->vertex(3) +
-                  quad->line(0)->child(0)->vertex(1) +
-                  quad->line(1)->child(0)->vertex(1) +
-                  quad->line(2)->child(0)->vertex(1) +
-                  quad->line(3)->child(0)->vertex(1)   ) / 8;
+                  3*(quad->line(0)->child(0)->vertex(1) +
+                     quad->line(1)->child(0)->vertex(1) +
+                     quad->line(2)->child(0)->vertex(1) +
+                     quad->line(3)->child(0)->vertex(1))   ) / 16;
          
                                             // now that we created the right
                                             // point, make up the four
@@ -5076,28 +5090,37 @@ void Triangulation<3>::execute_refinement ()
                    ExcTooFewVerticesAllocated());
            vertices_used[next_unused_vertex] = true;
            
-                                            // the new vertex is definitely in
-                                            // the interior, so we need not
-                                            // worry about the boundary.
-                                            // let it be the average of
-                                            // the 26 vertices surrounding
-                                            // it
+                                            // the new vertex is
+                                            // definitely in the
+                                            // interior, so we need
+                                            // not worry about the
+                                            // boundary.  let it be
+                                            // the average of the 26
+                                            // vertices surrounding
+                                            // it. weight these
+                                            // vertices in the same
+                                            // way as they are
+                                            // weighted in the
+                                            // @p{MappingQ::set_laplace_on_hex_vector}
+                                            // function, and like the
+                                            // new vertex at the
+                                            // center of the quad is
+                                            // weighted (see above)
            vertices[next_unused_vertex] = Point<dim>();
                                             // first add corners of hex
            for (unsigned int vertex=0;
                 vertex<GeometryInfo<dim>::vertices_per_cell; ++vertex)
-             vertices[next_unused_vertex] += hex->vertex(vertex);
+             vertices[next_unused_vertex] += hex->vertex(vertex) / 128;
                                             // now add center of lines
-           for (unsigned int line=0; line<12; ++line)
-             vertices[next_unused_vertex] += hex->line(line)->child(0)->vertex(1);
+           for (unsigned int line=0;
+                line<GeometryInfo<dim>::lines_per_cell; ++line)
+             vertices[next_unused_vertex] += hex->line(line)->child(0)->vertex(1) *
+                                             7./192.;
                                             // finally add centers of faces
            for (unsigned int face=0;
                 face<GeometryInfo<dim>::faces_per_cell; ++face)
-             vertices[next_unused_vertex] += hex->face(face)->child(0)->vertex(2);
-
-                                            // compute average
-           vertices[next_unused_vertex] /= 26;
-
+             vertices[next_unused_vertex] += hex->face(face)->child(0)->vertex(2) *
+                                             1./12.;
 
                                             // now that we created the right
                                             // point, make up the six
index 10dda95c9bb9484a616f08b57d354a8eb9989bed..ca2d8c3187b48cfeaf2e18f6f53a415e14ec7679 100644 (file)
@@ -111,6 +111,17 @@ documentation, etc</a>.
 <h3>deal.II</h3>
 
 <ol>
+  <li> <p>
+       Changed: when refining a hexahedron in 3d, the rules by which
+       the new vertices at the centers of the faces and at the center
+       of the cell are placed, are changed. They are changed in a way
+       as to minimize the distortion of the resulting cells from the
+       optimal shape and to make them look as much alike as possible
+       to generate a smoother grid.
+       <br>
+       (WB 2001/03/02)
+       </p>
+
   <li> <p>
        Fix: the <code
        class="member">DoFTools::compute_intergrid_constraints</code>
index f303f553fcb2ae33b041162f909d8ef0d98b8559..aa6377ae76a434513a0396d303a60b82b4dae472 100644 (file)
@@ -620,7 +620,7 @@ DEAL:Test1.dim3::Start
 232  0.375 0.625 0.375
 233  0.625 0.625 0.375
 234  0.375 0.625 0.625
-235  0.438 0.438 0.438
+235  0.437 0.437 0.437
 1 3 hex     1 28 40 29 30 41 46 42 
 2 3 hex     28 9 31 40 41 33 45 46 
 3 3 hex     40 31 21 32 46 45 37 44 
@@ -856,26 +856,26 @@ DEAL:Test2.dim3::Start
 103  0.750 1.00 0.250
 104  0.750 1.00 0.750
 105  0.250 1.00 0.750
-106  0.250 0.500 0.158
-107  0.750 0.500 0.158
-108  0.750 0.500 0.842
-109  0.250 0.500 0.842
+106  0.241 0.500 0.134
+107  0.759 0.500 0.134
+108  0.759 0.500 0.866
+109  0.241 0.500 0.866
 110  0.250 0.250 0.500
 111  0.750 0.250 0.500
 112  0.750 0.750 0.500
 113  0.250 0.750 0.500
-114  0.500 0.250 0.158
-115  0.500 0.750 0.158
-116  0.500 0.750 0.842
-117  0.500 0.250 0.842
-118  0.246 0.246 0.188
-119  0.754 0.246 0.188
-120  0.754 0.246 0.812
-121  0.246 0.246 0.812
-122  0.246 0.754 0.188
-123  0.754 0.754 0.188
-124  0.754 0.754 0.812
-125  0.246 0.754 0.812
+114  0.500 0.241 0.134
+115  0.500 0.759 0.134
+116  0.500 0.759 0.866
+117  0.500 0.241 0.866
+118  0.243 0.243 0.178
+119  0.757 0.243 0.178
+120  0.757 0.243 0.822
+121  0.243 0.243 0.822
+122  0.243 0.757 0.178
+123  0.757 0.757 0.178
+124  0.757 0.757 0.822
+125  0.243 0.757 0.822
 126  0.125 0.00 0.00
 127  0.375 0.00 0.00
 128  0.625 0.00 0.00
@@ -1074,22 +1074,22 @@ DEAL:Test2.dim3::Start
 321  0.375 1.00 0.750
 322  0.250 1.00 0.875
 323  0.125 1.00 0.750
-324  0.226 0.500 -0.0774
-325  0.375 0.500 0.113
-326  0.250 0.500 0.329
-327  0.125 0.500 0.204
-328  0.774 0.500 -0.0774
-329  0.875 0.500 0.204
-330  0.750 0.500 0.329
-331  0.625 0.500 0.113
-332  0.750 0.500 0.671
-333  0.875 0.500 0.796
-334  0.774 0.500 1.08
-335  0.625 0.500 0.887
-336  0.250 0.500 0.671
-337  0.375 0.500 0.887
-338  0.226 0.500 1.08
-339  0.125 0.500 0.796
+324  0.222 0.500 -0.0896
+325  0.371 0.500 0.101
+326  0.246 0.500 0.317
+327  0.121 0.500 0.192
+328  0.778 0.500 -0.0896
+329  0.879 0.500 0.192
+330  0.754 0.500 0.317
+331  0.629 0.500 0.101
+332  0.754 0.500 0.683
+333  0.879 0.500 0.808
+334  0.778 0.500 1.09
+335  0.629 0.500 0.899
+336  0.246 0.500 0.683
+337  0.371 0.500 0.899
+338  0.222 0.500 1.09
+339  0.121 0.500 0.808
 340  0.250 0.125 0.500
 341  0.375 0.250 0.500
 342  0.250 0.375 0.500
@@ -1106,70 +1106,70 @@ DEAL:Test2.dim3::Start
 353  0.375 0.750 0.500
 354  0.250 0.875 0.500
 355  0.125 0.750 0.500
-356  0.500 0.226 -0.0774
-357  0.500 0.375 0.113
-358  0.500 0.250 0.329
-359  0.500 0.125 0.204
-360  0.500 0.774 -0.0774
-361  0.500 0.875 0.204
-362  0.500 0.750 0.329
-363  0.500 0.625 0.113
-364  0.500 0.750 0.671
-365  0.500 0.875 0.796
-366  0.500 0.774 1.08
-367  0.500 0.625 0.887
-368  0.500 0.250 0.671
-369  0.500 0.375 0.887
-370  0.500 0.226 1.08
-371  0.500 0.125 0.796
-372  0.248 0.123 0.219
-373  0.373 0.248 0.173
-374  0.248 0.373 0.173
-375  0.123 0.248 0.219
-376  0.219 0.219 -0.0305
-377  0.248 0.248 0.344
-378  0.752 0.123 0.219
-379  0.877 0.248 0.219
-380  0.752 0.373 0.173
-381  0.627 0.248 0.173
-382  0.781 0.219 -0.0305
-383  0.752 0.248 0.344
-384  0.752 0.123 0.781
-385  0.877 0.248 0.781
-386  0.752 0.373 0.827
-387  0.627 0.248 0.827
-388  0.752 0.248 0.656
-389  0.781 0.219 1.03
-390  0.248 0.123 0.781
-391  0.373 0.248 0.827
-392  0.248 0.373 0.827
-393  0.123 0.248 0.781
-394  0.248 0.248 0.656
-395  0.219 0.219 1.03
-396  0.248 0.627 0.173
-397  0.373 0.752 0.173
-398  0.248 0.877 0.219
-399  0.123 0.752 0.219
-400  0.219 0.781 -0.0305
-401  0.248 0.752 0.344
-402  0.752 0.627 0.173
-403  0.877 0.752 0.219
-404  0.752 0.877 0.219
-405  0.627 0.752 0.173
-406  0.781 0.781 -0.0305
-407  0.752 0.752 0.344
-408  0.752 0.627 0.827
-409  0.877 0.752 0.781
-410  0.752 0.877 0.781
-411  0.627 0.752 0.827
-412  0.752 0.752 0.656
-413  0.781 0.781 1.03
-414  0.248 0.627 0.827
-415  0.373 0.752 0.827
-416  0.248 0.877 0.781
-417  0.123 0.752 0.781
-418  0.248 0.752 0.656
-419  0.219 0.781 1.03
+356  0.500 0.222 -0.0896
+357  0.500 0.371 0.101
+358  0.500 0.246 0.317
+359  0.500 0.121 0.192
+360  0.500 0.778 -0.0896
+361  0.500 0.879 0.192
+362  0.500 0.754 0.317
+363  0.500 0.629 0.101
+364  0.500 0.754 0.683
+365  0.500 0.879 0.808
+366  0.500 0.778 1.09
+367  0.500 0.629 0.899
+368  0.500 0.246 0.683
+369  0.500 0.371 0.899
+370  0.500 0.222 1.09
+371  0.500 0.121 0.808
+372  0.246 0.121 0.214
+373  0.371 0.242 0.156
+374  0.242 0.371 0.156
+375  0.121 0.246 0.214
+376  0.218 0.218 -0.0358
+377  0.246 0.246 0.339
+378  0.754 0.121 0.214
+379  0.879 0.246 0.214
+380  0.758 0.371 0.156
+381  0.629 0.242 0.156
+382  0.782 0.218 -0.0358
+383  0.754 0.246 0.339
+384  0.754 0.121 0.786
+385  0.879 0.246 0.786
+386  0.758 0.371 0.844
+387  0.629 0.242 0.844
+388  0.754 0.246 0.661
+389  0.782 0.218 1.04
+390  0.246 0.121 0.786
+391  0.371 0.242 0.844
+392  0.242 0.371 0.844
+393  0.121 0.246 0.786
+394  0.246 0.246 0.661
+395  0.218 0.218 1.04
+396  0.242 0.629 0.156
+397  0.371 0.758 0.156
+398  0.246 0.879 0.214
+399  0.121 0.754 0.214
+400  0.218 0.782 -0.0358
+401  0.246 0.754 0.339
+402  0.758 0.629 0.156
+403  0.879 0.754 0.214
+404  0.754 0.879 0.214
+405  0.629 0.758 0.156
+406  0.782 0.782 -0.0358
+407  0.754 0.754 0.339
+408  0.758 0.629 0.844
+409  0.879 0.754 0.786
+410  0.754 0.879 0.786
+411  0.629 0.758 0.844
+412  0.754 0.754 0.661
+413  0.782 0.782 1.04
+414  0.242 0.629 0.844
+415  0.371 0.758 0.844
+416  0.246 0.879 0.786
+417  0.121 0.754 0.786
+418  0.246 0.754 0.661
+419  0.218 0.782 1.04
 420  0.125 0.00 0.125
 421  0.375 0.00 0.125
 422  0.375 0.00 0.375
@@ -1266,18 +1266,18 @@ DEAL:Test2.dim3::Start
 513  0.375 1.00 0.625
 514  0.375 1.00 0.875
 515  0.125 1.00 0.875
-516  0.113 0.500 0.0238
-517  0.363 0.500 -0.113
-518  0.125 0.500 0.352
-519  0.637 0.500 -0.113
-520  0.887 0.500 0.0238
-521  0.875 0.500 0.352
-522  0.875 0.500 0.648
-523  0.887 0.500 0.976
-524  0.637 0.500 1.11
-525  0.125 0.500 0.648
-526  0.363 0.500 1.11
-527  0.113 0.500 0.976
+516  0.101 0.500 0.00204
+517  0.360 0.500 -0.122
+518  0.123 0.500 0.346
+519  0.640 0.500 -0.122
+520  0.899 0.500 0.00204
+521  0.877 0.500 0.346
+522  0.877 0.500 0.654
+523  0.899 0.500 0.998
+524  0.640 0.500 1.12
+525  0.123 0.500 0.654
+526  0.360 0.500 1.12
+527  0.101 0.500 0.998
 528  0.125 0.125 0.500
 529  0.375 0.125 0.500
 530  0.125 0.375 0.500
@@ -1290,170 +1290,170 @@ DEAL:Test2.dim3::Start
 537  0.125 0.625 0.500
 538  0.375 0.875 0.500
 539  0.125 0.875 0.500
-540  0.500 0.113 0.0238
-541  0.500 0.363 -0.113
-542  0.500 0.125 0.352
-543  0.500 0.637 -0.113
-544  0.500 0.887 0.0238
-545  0.500 0.875 0.352
-546  0.500 0.875 0.648
-547  0.500 0.887 0.976
-548  0.500 0.637 1.11
-549  0.500 0.125 0.648
-550  0.500 0.363 1.11
-551  0.500 0.113 0.976
-552  0.110 0.235 0.0473
-553  0.360 0.223 -0.0539
-554  0.374 0.249 0.337
-555  0.124 0.249 0.360
-556  0.124 0.124 0.235
-557  0.374 0.124 0.212
-558  0.374 0.374 0.143
-559  0.124 0.374 0.212
-560  0.235 0.110 0.0473
-561  0.223 0.360 -0.0539
-562  0.249 0.374 0.337
-563  0.249 0.124 0.360
-564  0.640 0.223 -0.0539
-565  0.890 0.235 0.0473
-566  0.876 0.249 0.360
-567  0.626 0.249 0.337
-568  0.626 0.124 0.212
-569  0.876 0.124 0.235
-570  0.876 0.374 0.212
-571  0.626 0.374 0.143
-572  0.765 0.110 0.0473
-573  0.777 0.360 -0.0539
-574  0.751 0.374 0.337
-575  0.751 0.124 0.360
-576  0.626 0.249 0.663
-577  0.876 0.249 0.640
-578  0.890 0.235 0.953
-579  0.640 0.223 1.05
-580  0.626 0.124 0.788
-581  0.876 0.124 0.765
-582  0.876 0.374 0.788
-583  0.626 0.374 0.857
-584  0.751 0.124 0.640
-585  0.751 0.374 0.663
-586  0.777 0.360 1.05
-587  0.765 0.110 0.953
-588  0.124 0.249 0.640
-589  0.374 0.249 0.663
-590  0.360 0.223 1.05
-591  0.110 0.235 0.953
-592  0.124 0.124 0.765
-593  0.374 0.124 0.788
-594  0.374 0.374 0.857
-595  0.124 0.374 0.788
-596  0.249 0.124 0.640
-597  0.249 0.374 0.663
-598  0.223 0.360 1.05
-599  0.235 0.110 0.953
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 1 3 hex     118 114 76 110 106 80 27 79 
 2 3 hex     114 119 111 76 80 107 77 27 
 3 3 hex     76 111 120 117 27 77 108 81 

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