MeshField::QuadraticTetrahedronShape Struct Reference

Quadratic (P2) shape functions for 3D tetrahedral elements. More...

#include <MeshField_Shape.hpp>

Public Member Functions
KOKKOS_INLINE_FUNCTION Kokkos::Array< Real, numNodes *meshEntDim >	getNodeParametricCoords () const
	Get parametric coordinates of element nodes. More...
KOKKOS_INLINE_FUNCTION Kokkos::Array< Real, numNodes >	getValues (Vector3 const &xi) const
	Evaluate quadratic shape functions at parametric coordinate. More...
KOKKOS_INLINE_FUNCTION Kokkos::Array< Real, meshEntDim *numNodes >	getLocalGradients (Vector3 const &xi) const
	Get gradients of quadratic shape functions in parametric coordinates. More...

Static Public Attributes
static const size_t	numNodes = 10
	Number of nodes (10 for quadratic tetrahedron)
static const size_t	meshEntDim = 3
	Mesh entity dimension (3D)
constexpr static Mesh_Topology	DofHolders [2] = {Vertex, Edge}
	DOFs at vertices and edges.
constexpr static size_t	NumDofHolders [2] = {4, 6}
	4 vertices, 6 edges
constexpr static size_t	DofsPerHolder [2] = {1, 1}
	1 DOF per vertex/edge
constexpr static size_t	Order = 2
	Polynomial order (quadratic)

Detailed Description

Quadratic (P2) shape functions for 3D tetrahedral elements.

Defines quadratic basis functions for a tetrahedral element with 10 nodes. Nodes are located at vertices and edge midpoints. Parametric coordinate range: xi0, xi1, xi2 [0, 1]

Node ordering:

• Nodes 0-3: Tetrahedron vertices
• Nodes 4-9: Edge midpoints

Shape functions and ordering from: Zienkiewicz, Taylor, and Zhu 'The Finite Element Method: Its Basis and Fundamentals', 2013

Definition at line 461 of file MeshField_Shape.hpp.

Member Function Documentation

getLocalGradients()

KOKKOS_INLINE_FUNCTION Kokkos::Array<Real, meshEntDim * numNodes> MeshField::QuadraticTetrahedronShape::getLocalGradients ( Vector3 const &  xi ) const

inline

Get gradients of quadratic shape functions in parametric coordinates.

Parameters

xi	Parametric coordinates (xi0, xi1, xi2) where xi_i [0,1]

Returns

Array of gradient vectors [dN0/dxi0, dN0/dxi1, dN0/dxi2, ..., dN9/dxi0, dN9/dxi1, dN9/dxi2]

Definition at line 532 of file MeshField_Shape.hpp.

getNodeParametricCoords()

KOKKOS_INLINE_FUNCTION Kokkos::Array<Real, numNodes * meshEntDim> MeshField::QuadraticTetrahedronShape::getNodeParametricCoords ( ) const

inline

Get parametric coordinates of element nodes.

Returns

Array of node coordinates for 10 nodes (4 at vertices, 6 at edge midpoints)

Definition at line 474 of file MeshField_Shape.hpp.

getValues()

KOKKOS_INLINE_FUNCTION Kokkos::Array<Real, numNodes> MeshField::QuadraticTetrahedronShape::getValues ( Vector3 const &  xi ) const

inline

Evaluate quadratic shape functions at parametric coordinate.

Parameters

xi	Parametric coordinates (xi0, xi1, xi2) where xi_i [0,1]

Returns

Array of 10 shape function values for quadratic tetrahedron N_i = L_i(2L_i - 1) for vertices (i=0,1,2,3) N_i = 4*L_j*L_k for edge midpoints (i=4-9) where L0=1-xi0-xi1-xi2, L1=xi0, L2=xi1, L3=xi2 are barycentric coordinates

Definition at line 502 of file MeshField_Shape.hpp.

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

• meshFields/src/MeshField_Shape.hpp