Element traits for 27-node triquadratic hexahedron (Hex27) More...

#include <Hex27.hpp>

Collaboration diagram for DNDS::Geom::Elem::ElementTraits< Hex27 >:

Static Public Member Functions
static constexpr ElemType	GetFaceType (t_index)
	Get the element type of a face.

static constexpr ElemType	GetBisectElemType (t_index)
	Get the element type of a sub-element after bisection.

Static Public Attributes
static constexpr ElemType	elemType = Hex27

static constexpr int	dim = 3

static constexpr int	order = 2

static constexpr int	numVertices = 8

static constexpr int	numNodes = 27

static constexpr int	numFaces = 6

static constexpr ParamSpace	paramSpace = HexSpace

static constexpr t_real	paramSpaceVol = 8.0

static constexpr std::array< t_real, 3 *27 >	standardCoords
	Standard coordinates of nodes in parametric space.

static constexpr std::array< std::array< t_index, 10 >, 6 >	faceNodes
	Node indices for each face (biquadratic quad)

static constexpr ElemType	elevatedType = UnknownElem
	Element type after order elevation (O2 has no higher elevation defined)

static constexpr int	numElevNodes = 0
	Number of additional nodes created during elevation (none for O2)

static constexpr int	numBisect = 8
	Number of sub-elements created when bisecting (8 Hex8 elements)

static constexpr int	numBisectVariants = 1
	Number of bisection variants (only 1 way to uniformly bisect)

static constexpr std::array< tBisectSub, 8 >	bisectElements
	Node indices for each sub-element created by bisection.

static constexpr int	vtkCellType = 25
	VTK cell type identifier (25 = VTK_TRIQUADRATIC_HEXAHEDRON)

static constexpr std::array< int, 20 >	vtkNodeOrder
	VTK node ordering map.

Detailed Description

Element traits for 27-node triquadratic hexahedron (Hex27)

Hex27 is a high-order 3D hexahedral element with:

8 corner nodes (vertices)
12 edge mid-nodes
6 face center nodes
1 body center node

Used for high-order finite element and spectral element methods.

Definition at line 920 of file Hex27.hpp.

Member Function Documentation

◆ GetBisectElemType()

static constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex27 >::GetBisectElemType ( t_index )

inlinestaticconstexpr

Get the element type of a sub-element after bisection.

Returns: Hex8 (all sub-elements are trilinear hexes)

Definition at line 1009 of file Hex27.hpp.

◆ GetFaceType()

static constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex27 >::GetFaceType ( t_index )

inlinestaticconstexpr

Get the element type of a face.

Returns: Quad9 (all faces are 9-node biquadratic quads)

Definition at line 970 of file Hex27.hpp.

Member Data Documentation

◆ bisectElements

constexpr std::array<tBisectSub, 8> DNDS::Geom::Elem::ElementTraits< Hex27 >::bisectElements

staticconstexpr

Initial value:

= {{
            {0, 8, 20, 11, 12, 21, 26, 24},     
            {8, 1, 9, 20, 21, 13, 22, 26},     
            {11, 20, 10, 3, 24, 26, 23, 15},   
            {20, 9, 2, 10, 26, 22, 14, 23},    
            {12, 21, 26, 24, 4, 16, 25, 19},   
            {21, 13, 22, 26, 16, 5, 17, 25},   
            {24, 26, 23, 15, 19, 25, 18, 7},   
            {26, 22, 14, 23, 25, 17, 6, 18}}}

Node indices for each sub-element created by bisection.

Bisecting creates 8 sub-hexes meeting at the body center node 26. Each sub-hex uses corners, edge mids, face centers, and body center.

Definition at line 1017 of file Hex27.hpp.

◆ dim

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::dim = 3

staticconstexpr

Definition at line 927 of file Hex27.hpp.

◆ elemType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex27 >::elemType = Hex27

staticconstexpr

Definition at line 926 of file Hex27.hpp.

◆ elevatedType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Hex27 >::elevatedType = UnknownElem

staticconstexpr

Element type after order elevation (O2 has no higher elevation defined)

Definition at line 990 of file Hex27.hpp.

◆ faceNodes

constexpr std::array<std::array<t_index, 10>, 6> DNDS::Geom::Elem::ElementTraits< Hex27 >::faceNodes

staticconstexpr

Initial value:

= {{
            {0, 3, 2, 1, 11, 10, 9, 8, 20},     
            {0, 1, 5, 4, 8, 13, 16, 12, 21},    
            {1, 2, 6, 5, 9, 14, 17, 13, 22},    
            {2, 3, 7, 6, 10, 15, 18, 14, 23},   
            {0, 4, 7, 3, 12, 19, 15, 11, 24},   
            {4, 5, 6, 7, 16, 17, 18, 19, 25}}}

Node indices for each face (biquadratic quad)

Each face has 9 nodes: 4 vertices + 4 edge mids + 1 face center

Definition at line 977 of file Hex27.hpp.

◆ numBisect

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numBisect = 8

staticconstexpr

Number of sub-elements created when bisecting (8 Hex8 elements)

Definition at line 1000 of file Hex27.hpp.

◆ numBisectVariants

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numBisectVariants = 1

staticconstexpr

Number of bisection variants (only 1 way to uniformly bisect)

Definition at line 1003 of file Hex27.hpp.

◆ numElevNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numElevNodes = 0

staticconstexpr

Number of additional nodes created during elevation (none for O2)

Definition at line 993 of file Hex27.hpp.

◆ numFaces

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numFaces = 6

staticconstexpr

Definition at line 931 of file Hex27.hpp.

◆ numNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numNodes = 27

staticconstexpr

Definition at line 930 of file Hex27.hpp.

◆ numVertices

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::numVertices = 8

staticconstexpr

Definition at line 929 of file Hex27.hpp.

◆ order

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::order = 2

staticconstexpr

Definition at line 928 of file Hex27.hpp.

◆ paramSpace

constexpr ParamSpace DNDS::Geom::Elem::ElementTraits< Hex27 >::paramSpace = HexSpace

staticconstexpr

Definition at line 932 of file Hex27.hpp.

◆ paramSpaceVol

constexpr t_real DNDS::Geom::Elem::ElementTraits< Hex27 >::paramSpaceVol = 8.0

staticconstexpr

Definition at line 933 of file Hex27.hpp.

◆ standardCoords

constexpr std::array<t_real, 3 * 27> DNDS::Geom::Elem::ElementTraits< Hex27 >::standardCoords

staticconstexpr

Initial value:

= {
            
            -1, -1, -1,    1, -1, -1,    1,  1, -1,   -1,  1, -1,
            -1, -1,  1,    1, -1,  1,    1,  1,  1,   -1,  1,  1,
            
             0, -1, -1,    1,  0, -1,    0,  1, -1,   -1,  0, -1,
            -1, -1,  0,    1, -1,  0,    1,  1,  0,   -1,  1,  0,
             0, -1,  1,    1,  0,  1,    0,  1,  1,   -1,  0,  1,
            
             0,  0, -1,    0, -1,  0,    1,  0,  0,    0,  1,  0,
            -1,  0,  0,    0,  0,  1,
            
             0,  0,  0}

Standard coordinates of nodes in parametric space.

Reference cube [-1,1]^3 with nodes: Nodes 0-7: corners (same as Hex8) Nodes 8-19: edge midpoints Nodes 20-25: face centers Node 26: body center

Definition at line 948 of file Hex27.hpp.

◆ vtkCellType

constexpr int DNDS::Geom::Elem::ElementTraits< Hex27 >::vtkCellType = 25

staticconstexpr

VTK cell type identifier (25 = VTK_TRIQUADRATIC_HEXAHEDRON)

Definition at line 1032 of file Hex27.hpp.

◆ vtkNodeOrder

constexpr std::array<int, 20> DNDS::Geom::Elem::ElementTraits< Hex27 >::vtkNodeOrder

staticconstexpr

Initial value:

= {
            0, 1, 2, 3, 4, 5, 6, 7,       
            8, 9, 10, 11,                 
            16, 17, 18, 19,               
            12, 13, 14, 15}

VTK node ordering map.

VTK has non-trivial node reordering for Hex27: VTK nodes 0-7 = corner nodes 0-7 VTK nodes 8-11 = bottom face edge mids 8-11 VTK nodes 12-15 = top face edge mids 16-19 VTK nodes 16-19 = vertical edge mids 12-15 VTK nodes 20-25 = face centers 21-26 (reordered!) Note: Only 20 nodes used by VTK (excludes some face centers)

Definition at line 1045 of file Hex27.hpp.

The documentation for this struct was generated from the following file:

/home/runner/work/DNDSR/DNDSR/src/Geom/Elements/Hex27.hpp

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ GetBisectElemType()

◆ GetFaceType()

Member Data Documentation

◆ bisectElements

◆ dim

◆ elemType

◆ elevatedType

◆ faceNodes

◆ numBisect

◆ numBisectVariants

◆ numElevNodes

◆ numFaces

◆ numNodes

◆ numVertices

◆ order

◆ paramSpace

◆ paramSpaceVol

◆ standardCoords

◆ vtkCellType

◆ vtkNodeOrder