Patched MeshTools::find_nodal_neighbors

[pbehne]

This PR updates MeshTools::find_nodal_neighbors to work correctly with higher order element types.

Refer to #4269 for two examples of incorrect results. The results for the same meshes, with this patch are listed below.

TRI6 example:

Node   Node id()=0, Point=(x,y,z)=(       0,        0,        0)
has neighbors:
    Node id()=3, Point=(x,y,z)=(     0.5,        0,        0)
    Node id()=5, Point=(x,y,z)=(     0.5,      0.5,        0)

Node   Node id()=1, Point=(x,y,z)=(       1,        0,        0)
has neighbors:
    Node id()=3, Point=(x,y,z)=(     0.5,        0,        0)
    Node id()=4, Point=(x,y,z)=(       1,      0.5,        0)

Node   Node id()=2, Point=(x,y,z)=(       1,        1,        0)
has neighbors:
    Node id()=4, Point=(x,y,z)=(       1,      0.5,        0)
    Node id()=5, Point=(x,y,z)=(     0.5,      0.5,        0)

Node   Node id()=3, Point=(x,y,z)=(     0.5,        0,        0)
has neighbors:
    Node id()=0, Point=(x,y,z)=(       0,        0,        0)
    Node id()=1, Point=(x,y,z)=(       1,        0,        0)

Node   Node id()=4, Point=(x,y,z)=(       1,      0.5,        0)
has neighbors:
    Node id()=1, Point=(x,y,z)=(       1,        0,        0)
    Node id()=2, Point=(x,y,z)=(       1,        1,        0)

Node   Node id()=5, Point=(x,y,z)=(     0.5,      0.5,        0)
has neighbors:
    Node id()=0, Point=(x,y,z)=(       0,        0,        0)
    Node id()=2, Point=(x,y,z)=(       1,        1,        0)

TET10 example:

Node   Node id()=0, Point=(x,y,z)=(       0,        0,        0)
has neighbors:
    Node id()=4, Point=(x,y,z)=(0.561231,        0,        0)
    Node id()=6, Point=(x,y,z)=(0.280616,  0.48604,        0)
    Node id()=7, Point=(x,y,z)=(0.280616, 0.162013, 0.458243)

Node   Node id()=1, Point=(x,y,z)=( 1.12246,        0,        0)
has neighbors:
    Node id()=4, Point=(x,y,z)=(0.561231,        0,        0)
    Node id()=5, Point=(x,y,z)=(0.841847,  0.48604,        0)
    Node id()=8, Point=(x,y,z)=(0.841847, 0.162013, 0.458243)

Node   Node id()=2, Point=(x,y,z)=(0.561231, 0.972081,        0)
has neighbors:
    Node id()=5, Point=(x,y,z)=(0.841847,  0.48604,        0)
    Node id()=6, Point=(x,y,z)=(0.280616,  0.48604,        0)
    Node id()=9, Point=(x,y,z)=(0.561231, 0.648054, 0.458243)

Node   Node id()=3, Point=(x,y,z)=(0.561231, 0.324027, 0.916486)
has neighbors:
    Node id()=7, Point=(x,y,z)=(0.280616, 0.162013, 0.458243)
    Node id()=8, Point=(x,y,z)=(0.841847, 0.162013, 0.458243)
    Node id()=9, Point=(x,y,z)=(0.561231, 0.648054, 0.458243)

Node   Node id()=4, Point=(x,y,z)=(0.561231,        0,        0)
has neighbors:
    Node id()=0, Point=(x,y,z)=(       0,        0,        0)
    Node id()=1, Point=(x,y,z)=( 1.12246,        0,        0)

Node   Node id()=5, Point=(x,y,z)=(0.841847,  0.48604,        0)
has neighbors:
    Node id()=1, Point=(x,y,z)=( 1.12246,        0,        0)
    Node id()=2, Point=(x,y,z)=(0.561231, 0.972081,        0)

Node   Node id()=6, Point=(x,y,z)=(0.280616,  0.48604,        0)
has neighbors:
    Node id()=0, Point=(x,y,z)=(       0,        0,        0)
    Node id()=2, Point=(x,y,z)=(0.561231, 0.972081,        0)

Node   Node id()=7, Point=(x,y,z)=(0.280616, 0.162013, 0.458243)
has neighbors:
    Node id()=0, Point=(x,y,z)=(       0,        0,        0)
    Node id()=3, Point=(x,y,z)=(0.561231, 0.324027, 0.916486)

Node   Node id()=8, Point=(x,y,z)=(0.841847, 0.162013, 0.458243)
has neighbors:
    Node id()=1, Point=(x,y,z)=( 1.12246,        0,        0)
    Node id()=3, Point=(x,y,z)=(0.561231, 0.324027, 0.916486)

Node   Node id()=9, Point=(x,y,z)=(0.561231, 0.648054, 0.458243)
has neighbors:
    Node id()=2, Point=(x,y,z)=(0.561231, 0.972081,        0)
    Node id()=3, Point=(x,y,z)=(0.561231, 0.324027, 0.916486)

Closes #4269

[moosebuild]

Job Coverage, step Generate coverage on 874c3ac wanted to post the following:

Coverage

	034308	#4270 874c3a
	Total	Total	+/-	New
Rate	64.96%	64.95%	-0.01%	100.00%
Hits	76814	76808	-6	9
Misses	41432	41441	+9	0

Diff coverage report

Full coverage report

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