MeshField::LinearTetrahedronShape Struct Reference

[QuadraticTriangleShape] 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 shape functions at parametric coordinate. More...
KOKKOS_INLINE_FUNCTION Kokkos::Array< Real, meshEntDim *numNodes >	getLocalGradients (Vector3 const &) const
	Get gradients of shape functions in parametric coordinates @detail gradients are constant - ignoring parametric coord input. More...

Static Public Attributes
static const size_t	numNodes = 4
	Number of nodes (4 for linear tetrahedron)
static const size_t	meshEntDim = 3
	Mesh entity dimension (3D)
constexpr static Mesh_Topology	DofHolders [1] = {Vertex}
	DOFs located at vertices.
constexpr static size_t	Order = 1
	Polynomial order (linear)

Detailed Description

[QuadraticTriangleShape]

Linear (P1) shape functions for 3D tetrahedral elements

Defines linear basis functions for a tetrahedral element with 4 nodes. Parametric coordinate range: xi0, xi1, xi2 [0, 1]

Node ordering:

• Node 0 at (0, 0, 0)
• Node 1 at (1, 0, 0)
• Node 2 at (0, 1, 0)
• Node 3 at (0, 0, 1)

Shape functions use barycentric coordinates L0, L1, L2, L3 where L0 = 1-xi0-xi1-xi2, L1 = xi0, L2 = xi1, L3 = xi2

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

Definition at line 388 of file MeshField_Shape.hpp.

Member Function Documentation

getLocalGradients()

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

inline

Get gradients of shape functions in parametric coordinates @detail gradients are constant - ignoring parametric coord input.

Returns

Array of constant gradients [dN0/dxi0, dN0/dxi1, dN0/dxi2, dN1/dxi0, ...] Constant gradients: [[-1,-1,-1], [1,0,0], [0,1,0], [0,0,1]]

Definition at line 436 of file MeshField_Shape.hpp.

getNodeParametricCoords()

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

inline

Get parametric coordinates of element nodes.

Returns

Array of node coordinates for 4 vertices

Definition at line 399 of file MeshField_Shape.hpp.

getValues()

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

inline

Evaluate shape functions at parametric coordinate.

Parameters

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

Returns

Array of shape function values [N0, N1, N2, N3] = [L0, L1, L2, L3] where L0 = 1-xi0-xi1-xi2, L1 = xi0, L2 = xi1, L3 = xi2

Definition at line 415 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