Reference cells
The reference cells are used to i) define grid cells, ii) define shape functions, and iii) define quadrature rules. The numbering of vertices, edges, faces are visualized below. See also FerriteViz.elementinfo.
AbstractRefShape subtypes
Ferrite.AbstractRefShape — TypeAbstractRefShape{refdim}Supertype for all reference shapes, with reference dimension refdim. Reference shapes are used to define grid cells, shape functions, and quadrature rules. Currently existing reference shapes are: RefLine, RefTriangle, RefQuadrilateral, RefTetrahedron, RefHexahedron, RefPrism.
Ferrite.RefLine — TypeRefLine <: AbstractRefShape{1}Reference line/interval, reference dimension 1.
----------------+--------------------
Vertex numbers: | Vertex coordinates:
1-------2 | v1: 𝛏 = (-1.0,)
--> ξ₁ | v2: 𝛏 = ( 1.0,)
----------------+--------------------
Face numbers: | Face identifiers:
1-------2 | f1: (v1,)
| f2: (v2,)
----------------+--------------------Ferrite.RefTriangle — TypeRefTriangle <: AbstractRefShape{2}Reference triangle, reference dimension 2.
----------------+--------------------
Vertex numbers: | Vertex coordinates:
2 |
| \ | v1: 𝛏 = (1.0, 0.0)
| \ | v2: 𝛏 = (0.0, 1.0)
ξ₂^ | \ | v3: 𝛏 = (0.0, 0.0)
| 3-------1 |
+--> ξ₁ |
----------------+--------------------
Face numbers: | Face identifiers:
+ |
| \ | f1: (v1, v2)
2 1 | f2: (v2, v3)
| \ | f3: (v3, v1)
+---3---+ |
----------------+--------------------Ferrite.RefQuadrilateral — TypeRefQuadrilateral <: AbstractRefShape{2}Reference quadrilateral, reference dimension 2.
----------------+---------------------
Vertex numbers: | Vertex coordinates:
4-------3 |
| | | v1: 𝛏 = (-1.0, -1.0)
| | | v2: 𝛏 = ( 1.0, -1.0)
ξ₂^ | | | v3: 𝛏 = ( 1.0, 1.0)
| 1-------2 | v4: 𝛏 = (-1.0, 1.0)
+--> ξ₁ |
----------------+---------------------
Face numbers: | Face identifiers:
+---3---+ | f1: (v1, v2)
| | | f2: (v2, v3)
4 2 | f3: (v3, v4)
| | | f4: (v4, v1)
+---1---+ |
----------------+---------------------Ferrite.RefTetrahedron — TypeRefTetrahedron <: AbstractRefShape{3}Reference tetrahedron, reference dimension 3.
---------------------------------------+-------------------------
Vertex numbers: | Vertex coordinates:
4 4 |
^ ξ₃ / \ /| \ | v1: 𝛏 = (0.0, 0.0, 0.0)
| / \ / | \ | v2: 𝛏 = (1.0, 0.0, 0.0)
+-> ξ₂ / \ / 1___ \ | v3: 𝛏 = (0.0, 1.0, 0.0)
/ / __--3 / / __‾-3 | v4: 𝛏 = (0.0, 0.0, 1.0)
ξ₁ 2 __--‾‾ 2/__--‾‾ |
---------------------------------------+-------------------------
Edge numbers: | Edge identifiers:
+ + | e1: (v1, v2)
/ \ /| \ | e2: (v2, v3)
5 / \ 6 5 / |4 \ 6 | e3: (v3, v1)
/ \ / +__3 \ | e4: (v1, v4)
/ __--+ / /1 __‾-+ | e5: (v2, v4)
+ __--‾‾2 +/__--‾‾2 | e6: (v3, v4)
---------------------------------------+-------------------------
Face numbers: | Face identifiers:
+ + |
/ \ /| \ | f1: (v1, v3, v2)
/ \ / | 4 \ | f2: (v1, v2, v4)
/ 3 \ /2 +___ \ | f3: (v2, v3, v4)
/ __--+ / / 1 __‾-+ | f4: (v1, v4, v3)
+ __--‾‾ +/__--‾‾ |
---------------------------------------+-------------------------Ferrite.RefHexahedron — TypeRefHexahedron <: AbstractRefShape{3}Reference hexahedron, reference dimension 3.
-----------------------------------------+----------------------------
Vertex numbers: | Vertex coordinates:
5--------8 5--------8 | v1: 𝛏 = (-1.0, -1.0, -1.0)
/ /| /| | | v2: 𝛏 = ( 1.0, -1.0, -1.0)
/ / | / | | | v3: 𝛏 = ( 1.0, 1.0, -1.0)
^ ξ₃ 6--------7 | 6 | | | v4: 𝛏 = (-1.0, 1.0, -1.0)
| | | 4 | 1--------4 | v5: 𝛏 = (-1.0, -1.0, 1.0)
+-> ξ₂ | | / | / / | v6: 𝛏 = ( 1.0, -1.0, 1.0)
/ | |/ |/ / | v7: 𝛏 = ( 1.0, 1.0, 1.0)
ξ₁ 2--------3 2--------3 | v8: 𝛏 = (-1.0, 1.0, 1.0)
-----------------------------------------+-----------------------------
Edge numbers: | Edge identifiers:
+----8---+ +----8---+ |
5/ /| 5/| | | e1: (v1, v2), e2: (v2, v3)
/ 7/ |12 / |9 12| | e3: (v3, v4), e4: (v4, v1)
+----6---+ | + | | | e5: (v5, v6), e6: (v6, v7)
| | + | +---4----+ | e7: (v7, v8), e8: (v8, v5)
10| 11| / 10| /1 / | e9: (v1, v5), e10: (v2, v6)
| |/3 |/ /3 | e11: (v3, v7), e12: (v4, v8)
+---2----+ +---2----+ |
-----------------------------------------+-----------------------------
Face numbers: | Face identifiers:
+--------+ +--------+ |
/ 6 /| /| | | f1: (v1, v4, v3, v2)
/ / | / | 5 | | f2: (v1, v2, v6, v5)
+--------+ 4| + | | | f3: (v2, v3, v7, v6)
| | + |2 +--------+ | f4: (v3, v4, v8, v7)
| 3 | / | / / | f5: (v1, v5, v8, v4)
| |/ |/ 1 / | f6: (v5, v6, v7, v8)
+--------+ +--------+ |
-----------------------------------------+-----------------------------Ferrite.RefPrism — TypeRefPrism <: AbstractRefShape{3}Reference prism, reference dimension 3.
-----------------------------------------+----------------------------
Vertex numbers: | Vertex coordinates:
4-------/6 4--------6 |
/ / | /| | | v1: 𝛏 = (0.0, 0.0, 0.0)
/ / | / | | | v2: 𝛏 = (1.0, 0.0, 0.0)
^ ξ₃ 5 / | 5 | | | v3: 𝛏 = (0.0, 1.0, 0.0)
| | /3 | 1-------/3 | v4: 𝛏 = (0.0, 0.0, 1.0)
+-> ξ₂ | / | / / | v5: 𝛏 = (1.0, 0.0, 1.0)
/ | / |/ / | v6: 𝛏 = (0.0, 1.0, 1.0)
ξ₁ 2 / 2 / |
-----------------------------------------+----------------------------
Edge numbers: | Edge identifiers:
+---8---/+ +---8----+ |
7/ / | 7/| | | e1: (v2, v1), e2: (v1, v3)
/ / 9 |6 / |3 |6 | e3: (v1, v4), e4: (v3, v2)
+ / | + | | | e5: (v2, v5), e6: (v3, v6)
| /+ | +--2----/+ | e7: (v4, v5), e8: (v4, v6)
5| / 5| /1 / | e9: (v6, v5)
| / 4 |/ / 4 |
+ / + / |
-----------------------------------------+----------------------------
Face numbers: | Face identifiers:
+-------/+ +--------+ |
/ 5 / | /| | | f1: (v1, v3, v2)
/ / | / | 3 | | f2: (v1, v2, v5, v4)
+ / | + | | | f3: (v3, v1, v4, v6)
| 4 /+ |2 +-------/+ | f4: (v2, v3, v6, v5)
| / | / 1 / | f5: (v4, v5, v6)
| / |/ / |
+ / + / |
-----------------------------------------+----------------------------