Element traits for 9-node biquadratic quadrilateral (Quad9) More...

#include <Quad9.hpp>

Collaboration diagram for DNDS::Geom::Elem::ElementTraits< Quad9 >:

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

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

Static Public Attributes
static constexpr ElemType	elemType = Quad9

static constexpr int	dim = 2

static constexpr int	order = 2

static constexpr int	numVertices = 4

static constexpr int	numNodes = 9

static constexpr int	numFaces = 4

static constexpr ParamSpace	paramSpace = QuadSpace

static constexpr t_real	paramSpaceVol = 4.0

static constexpr std::array< t_real, 3 *9 >	standardCoords
	Standard coordinates of nodes in parametric space.

static constexpr std::array< std::array< t_index, 10 >, 4 >	faceNodes
	Node indices for each face (edge)

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 = 4
	Number of sub-elements created when bisecting (4 Quad4 elements)

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

static constexpr std::array< tBisectSub, 4 >	bisectElements
	Node indices for each sub-element created by bisection.

static constexpr int	vtkCellType = 23
	VTK cell type identifier (23 = VTK_QUADRATIC_QUAD)

static constexpr std::array< int, 8 >	vtkNodeOrder = {0, 1, 2, 3, 4, 5, 6, 7}
	VTK node ordering map.

Detailed Description

Element traits for 9-node biquadratic quadrilateral (Quad9)

Quad9 is a high-order 2D quadrilateral element with:

4 corner nodes (vertices)
4 edge mid-nodes
1 interior node at the center

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

Definition at line 194 of file Quad9.hpp.

Member Function Documentation

◆ GetBisectElemType()

static constexpr ElemType DNDS::Geom::Elem::ElementTraits< Quad9 >::GetBisectElemType ( t_index )

inlinestaticconstexpr

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

Returns: Quad4 (all sub-elements are bilinear quads)

Definition at line 281 of file Quad9.hpp.

◆ GetFaceType()

static constexpr ElemType DNDS::Geom::Elem::ElementTraits< Quad9 >::GetFaceType ( t_index )

inlinestaticconstexpr

Get the element type of a face (edge)

Returns: Line3 (all edges are quadratic lines with 3 nodes)

Definition at line 240 of file Quad9.hpp.

Member Data Documentation

◆ bisectElements

constexpr std::array<tBisectSub, 4> DNDS::Geom::Elem::ElementTraits< Quad9 >::bisectElements

staticconstexpr

Initial value:

= {{
            {0, 4, 8, 7},    
            {4, 1, 5, 8},    
            {7, 8, 6, 3},    
            {8, 5, 2, 6}}}

Node indices for each sub-element created by bisection.

Bisecting creates 4 sub-quads meeting at the center node 8: Sub-element 0: bottom-left quad Sub-element 1: bottom-right quad Sub-element 2: top-left quad Sub-element 3: top-right quad

Definition at line 292 of file Quad9.hpp.

◆ dim

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::dim = 2

staticconstexpr

Definition at line 201 of file Quad9.hpp.

◆ elemType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Quad9 >::elemType = Quad9

staticconstexpr

Definition at line 200 of file Quad9.hpp.

◆ elevatedType

constexpr ElemType DNDS::Geom::Elem::ElementTraits< Quad9 >::elevatedType = UnknownElem

staticconstexpr

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

Definition at line 262 of file Quad9.hpp.

◆ faceNodes

constexpr std::array<std::array<t_index, 10>, 4> DNDS::Geom::Elem::ElementTraits< Quad9 >::faceNodes

staticconstexpr

Initial value:

= {{
            {0, 1, 4},     
            {1, 2, 5},     
            {2, 3, 6},     
            {3, 0, 7}}}

Node indices for each face (edge)

Each edge has 3 nodes: 2 vertices + 1 midpoint Edge 0: nodes 0-1-4 (bottom) Edge 1: nodes 1-2-5 (right) Edge 2: nodes 2-3-6 (top) Edge 3: nodes 3-0-7 (left)

Definition at line 251 of file Quad9.hpp.

◆ numBisect

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numBisect = 4

staticconstexpr

Number of sub-elements created when bisecting (4 Quad4 elements)

Definition at line 272 of file Quad9.hpp.

◆ numBisectVariants

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numBisectVariants = 1

staticconstexpr

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

Definition at line 275 of file Quad9.hpp.

◆ numElevNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numElevNodes = 0

staticconstexpr

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

Definition at line 265 of file Quad9.hpp.

◆ numFaces

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numFaces = 4

staticconstexpr

Definition at line 205 of file Quad9.hpp.

◆ numNodes

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numNodes = 9

staticconstexpr

Definition at line 204 of file Quad9.hpp.

◆ numVertices

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::numVertices = 4

staticconstexpr

Definition at line 203 of file Quad9.hpp.

◆ order

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::order = 2

staticconstexpr

Definition at line 202 of file Quad9.hpp.

◆ paramSpace

constexpr ParamSpace DNDS::Geom::Elem::ElementTraits< Quad9 >::paramSpace = QuadSpace

staticconstexpr

Definition at line 206 of file Quad9.hpp.

◆ paramSpaceVol

constexpr t_real DNDS::Geom::Elem::ElementTraits< Quad9 >::paramSpaceVol = 4.0

staticconstexpr

Definition at line 207 of file Quad9.hpp.

◆ standardCoords

constexpr std::array<t_real, 3 * 9> DNDS::Geom::Elem::ElementTraits< Quad9 >::standardCoords

staticconstexpr

Initial value:

Standard coordinates of nodes in parametric space.

Reference square [-1,1] x [-1,1] with nodes: Nodes 0-3: corners (same as Quad4) Nodes 4-7: edge midpoints Node 8: center (0, 0)

Definition at line 221 of file Quad9.hpp.

◆ vtkCellType

constexpr int DNDS::Geom::Elem::ElementTraits< Quad9 >::vtkCellType = 23

staticconstexpr

VTK cell type identifier (23 = VTK_QUADRATIC_QUAD)

Definition at line 303 of file Quad9.hpp.

◆ vtkNodeOrder

constexpr std::array<int, 8> DNDS::Geom::Elem::ElementTraits< Quad9 >::vtkNodeOrder = {0, 1, 2, 3, 4, 5, 6, 7}

staticconstexpr

VTK node ordering map.

VTK uses 8 nodes for quadratic quad (excludes interior node 8): VTK nodes 0-3 = corner nodes 0-3 VTK nodes 4-7 = edge mid-nodes 4-7

Definition at line 312 of file Quad9.hpp.

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

/home/runner/work/DNDSR/DNDSR/src/Geom/Elements/Quad9.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