#include <BB_Tetrahedron.hpp>

Inheritance diagram for geos::finiteElement::BB_Tetrahedron< ORDER >:

Public Member Functions
virtual	~BB_Tetrahedron ()=default

virtual GEOS_HOST_DEVICE localIndex	getNumQuadraturePoints () const override
	Virtual getter for the number of quadrature points per element. More...

GEOS_HOST_DEVICE virtual GEOS_FORCE_INLINE localIndex	getNumSupportPoints () const override
	Virtual getter for the number of support points per element. More...

GEOS_HOST_DEVICE virtual GEOS_FORCE_INLINE localIndex	getMaxSupportPoints () const override
	Get the maximum number of support points for this element. More...

Public Member Functions inherited from geos::finiteElement::FiniteElementBase
	FiniteElementBase ()=default
	Default Constructor.

GEOS_HOST_DEVICE	FiniteElementBase (FiniteElementBase const &source)
	Copy Constructor. More...

	FiniteElementBase (FiniteElementBase &&)=default
	Default Move constructor.

FiniteElementBase &	operator= (FiniteElementBase const &)=delete
	Deleted copy assignment operator. More...

FiniteElementBase &	operator= (FiniteElementBase &&)=delete
	Deleted move assignment operator. More...

virtual GEOS_HOST_DEVICE	~FiniteElementBase ()
	Destructor.

template<typename LEAF , typename SUBREGION_TYPE >
GEOS_HOST_DEVICE void	setup (localIndex const &cellIndex, typename LEAF::template MeshData< SUBREGION_TYPE > const &meshData, typename LEAF::StackVariables &stack) const
	Abstract setup method, possibly computing cell-dependent properties. More...

template<typename LEAF >
GEOS_HOST_DEVICE localIndex	numSupportPoints (typename LEAF::StackVariables const &stack) const
	Getter for the number of support points per element. More...

template<typename LEAF >
GEOS_HOST_DEVICE real64	getGradN (localIndex const k, localIndex const q, real64 const (&X)[LEAF::maxSupportPoints][3], real64(&gradN)[LEAF::maxSupportPoints][3]) const
	Get the shape function gradients. More...

template<typename LEAF >
GEOS_HOST_DEVICE real64	getGradN (localIndex const k, localIndex const q, real64 const (&X)[LEAF::maxSupportPoints][3], typename LEAF::StackVariables const &stack, real64(&gradN)[LEAF::maxSupportPoints][3]) const
	Get the shape function gradients. More...

template<typename LEAF >
GEOS_HOST_DEVICE real64	getGradN (localIndex const k, localIndex const q, int const X, real64(&gradN)[LEAF::maxSupportPoints][3]) const
	Get the shape function gradients. More...

template<typename LEAF >
GEOS_HOST_DEVICE real64	getGradN (localIndex const k, localIndex const q, int const X, typename LEAF::StackVariables const &stack, real64(&gradN)[LEAF::maxSupportPoints][3]) const
	Get the shape function gradients. More...

template<typename LEAF , localIndex NUMDOFSPERTRIALSUPPORTPOINT, bool UPPER = false>
GEOS_HOST_DEVICE void	addGradGradStabilizationMatrix (typename LEAF::StackVariables const &stack, real64(&matrix)[LEAF::maxSupportPoints NUMDOFSPERTRIALSUPPORTPOINT][LEAF::maxSupportPoints NUMDOFSPERTRIALSUPPORTPOINT], real64 const scaleFactor=1.0) const
	Add stabilization of grad-grad bilinear form to input matrix. More...

template<typename LEAF , localIndex NUMDOFSPERTRIALSUPPORTPOINT>
GEOS_HOST_DEVICE GEOS_FORCE_INLINE void	addEvaluatedGradGradStabilizationVector (typename LEAF::StackVariables const &stack, real64 const (&dofs)[LEAF::maxSupportPoints][NUMDOFSPERTRIALSUPPORTPOINT], real64(&targetVector)[LEAF::maxSupportPoints][NUMDOFSPERTRIALSUPPORTPOINT], real64 const scaleFactor=1.0) const
	Add a grad-grad stabilization operator evaluated at a provided vector of dofs to input vector. More...

void	setGradNView (arrayView4d< real64 const > const &source)
	Sets m_viewGradN equal to an input view. More...

void	setDetJView (arrayView2d< real64 const > const &source)
	Sets m_viewDetJ equal to an input view. More...

arrayView4d< real64 const >	getGradNView () const
	Getter for m_viewGradN. More...

arrayView2d< real64 const >	getDetJView () const
	Getter for m_viewDetJ. More...

Static Public Member Functions
GEOS_HOST_DEVICE static GEOS_FORCE_INLINE localIndex	getNumQuadraturePoints (StackVariables const &stack)
	Get the number of quadrature points. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE localIndex	getNumSupportPoints (StackVariables const &stack)
	Get the number of support points. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64	jacobianDeterminant (real64 const (&X)[4][3])
	Returns the determinant of the Jacobian of the element. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64	faceJacobianDeterminant (localIndex face, real64 const (&X)[4][3])
	Calculate the determinant of the jacobian on the face opposite to the given vertex. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcN (localIndex const, real64(&N)[numNodes])
	Calculate shape functions values for each support point at a quadrature point. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcN (localIndex const q, StackVariables const &stack, real64(&N)[numNodes])
	Calculate shape functions values for each support point at a quadrature point. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcN (real64 const (&lambda)[4], real64(&N)[numNodes])
	Calculate shape functions values at a single point using De Casteljau's algorithm. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcN (real64 const (&X)[4][3], real64 const (&coords)[3], real64(&N)[numNodes])
	Calculate shape functions values at a single point, given the coordinates of the tetrahedron vertices, using De Casteljau's algorithm. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcNandGradN (real64 const (&lambda)[4], real64 const (&N)[numNodes], real64(&gradN)[numNodes][4])
	Calculate the values and derivatives of shape functions with respect to barycentric coordinates at a single point using De Casteljau's algorithm. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	calcNandGradN (real64 const (&X)[4][3], real64 const (&coords)[3], real64(&N)[numNodes], real64(&gradN)[numNodes][4])
	Calculate the shape functions values and derivatives at a single point, given the coorginates of the tetrahedron vertices, using De Casteljau's algorithm. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64	calcGradN (localIndex const q, real64 const (&X)[numNodes][3], real64(&gradN)[numNodes][3])
	Calculate the shape functions derivatives wrt the physical coordinates. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64	calcGradN (localIndex const q, real64 const (&X)[numNodes][3], StackVariables const &stack, real64(&gradN)[numNodes][3])
	Calculate the shape functions derivatives wrt the physical coordinates. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	integralTerm (const int a, const int b, const int c)
	Computes a! / ( b! * c! ) with b + c >= a >= b, c. More...

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64	correctionFactorDerivative (int const i1, int const j1, int const k1, int const l1, int const i2, int const j2, int const k2, int const l2, int const dim)
	Computes the correction factor for the superposition integral in case a function has been derived once. The indices of the original function are ii1, j1, k1 and l1, and those of the once-derived one are i2, j2, k2 and l2. More...

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64	computeSuperpositionIntegral (const int i1, const int j1, const int k1, const int l1, const int i2, const int j2, const int k2, const int l2)
	Computes the superposition integral between Bernstein-Bézier functions indexed by (i1, j1, k1, l1) and (i1, j2, k2, l2) More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	computeFaceSuperpositionIntegral (const int i1, const int j1, const int k1, const int i2, const int j2, const int k2)
	Computes the superposition integral over a face between Bernstein-Bézier functions whose indices are given by (i1, j1, k1, l1=0 ) and (i1, j2, k2, l2=0) More...

template<int I, int J, int K>
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int	dofIndex ()
	Computes the local degree of freedom index given the shape function indices (i, j, k, l) for each vertex. Only i, j and k are needed since i + j + k + l = order. More...

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int	dofIndex (const int i, const int j, const int k)
	Computes the local degree of freedom index given the shape function indices (i, j, k, l) for each vertex. Only i, j and k are needed since i + j + k + l = order This version takes indices as parameters and can be called with non-constexpr index values. More...

template<int C, int VTX>
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int	indexToIJKL ()
	Computes the local degree of freedom index given the shape function indices for each vertex. More...

template<typename FUNC , int... Is>
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	loop_impl (FUNC &&func, std::integer_sequence< int, Is... >)
	Helper function for static for loop. More...

template<int N, typename FUNC >
static constexpr GEOS_HOST_DEVICE void	loop (FUNC const &func)
	Helper function for static for loop. More...

template<typename FUNC >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	barycentricCoordinateLoop (FUNC &&func)
	Helper function for loop over barycentric coordinates. More...

template<typename FUNC >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	basisLoop (FUNC &&func)
	Helper function for loop over tet basis functions. More...

template<int c1, int i1, int j1, int k1, int l1, typename F , int... Is>
static constexpr GEOS_HOST_DEVICE void	call_matching_cases (F &&func, std::integer_sequence< int, Is... >)
	Helper function for loop over tet basis functions that have one index in a given set of indices. If multiple indices are in the given list, the callback is called multiple times. This herlper is useful to avoid too much fold operations. More...

template<int... Is, typename FUNC >
static constexpr GEOS_HOST_DEVICE void	conditionalBasisLoop (FUNC const &func)
	Helper function for loop over tet basis functions that have one index in a given set of indices. If multiple indices are in the given list, the callback is called multiple times. More...

template<typename FUNC >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	faceBarycentricCoordinateLoop (FUNC &&func)
	Helper function for loop over barycentric coordinates of a face. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	computeReferenceMassMatrix (arraySlice2d< real64 > const &m)
	Computes the reference mass matrix, i.e., the superposition matrix of the shape functions in barycentric coordinates. The real-world mass matrix can be obtained by using the multiplying this matrix by the determinant of the Jacobian. More...

template<typename DAMPING >
GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	computeReferenceDampingMatrix (real64(&d)[numNodes][numNodes], bool const face1Damped, bool const face2Damped, bool const face3Damped, bool const face4Damped)
	Computes the reference damping matrix, i.e., the superposition matrix of the shape functions in barycentric coordinates over faces. The real-world mass matrix can be obtained by using the multiplying this matrix by the determinant of the face Jacobian. More...

template<typename FUNC >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	computeMassTerm (real64 const (&X)[4][3], FUNC &&func)
	Computes the non-zero contributions inside the element of the mass matrix M, i.e., the superposition matrix of shape functions. More...

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64	computeFluxDerivativeFactor (real64 const (&X)[4][3], int x1, int x2, int o1, int o2)
	Function to compute the factor for the flux derivative term. More...

template<typename FUNC >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	computeStiffnessTerm (real64 const (&X)[4][3], FUNC &&func)
	Computes the non-zero contributions inside the element of the stiffness matrix R, i.e., the superposition matrix of first derivatives of shape functions. More...

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64	edgeLength2 (localIndex i1, localIndex i2, real64 const (&X)[4][3])

template<typename FUNCP , typename FUNCF >
GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void	computeSurfaceTerms (real64 const (&X)[4][3], FUNCP &&funcP, FUNCF &&funcF)
	Computes the non-zero contributions inside the element of the surface terms, including the value of the superposition integral of basis functions (used for the penalty and damping terms) and the superposition integral of the derivative of a function with the value of the other, used for the flux terms. More...

Static Public Member Functions inherited from geos::finiteElement::FiniteElementBase
template<typename SUBREGION_TYPE >
static void	fillMeshData (NodeManager const &nodeManager, EdgeManager const &edgeManager, FaceManager const &faceManager, SUBREGION_TYPE const &cellSubRegion, MeshData< SUBREGION_TYPE > &meshData)
	Method to fill a MeshData object. More...

template<typename LEAF , typename SUBREGION_TYPE >
static void	initialize (NodeManager const &nodeManager, EdgeManager const &edgeManager, FaceManager const &faceManager, SUBREGION_TYPE const &cellSubRegion, typename LEAF::template MeshData< SUBREGION_TYPE > &meshData)
	Abstract initialization method. More...

template<typename SUBREGION_TYPE >
GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	setupStack (localIndex const &cellIndex, MeshData< SUBREGION_TYPE > const &meshData, StackVariables &stack)
	Empty setup method. More...

template<int N>
constexpr static GEOS_HOST_DEVICE PDEUtilities::FunctionSpace	getFunctionSpace ()
	Getter for the function space. More...

template<localIndex NUMDOFSPERTRIALSUPPORTPOINT, localIndex MAXSUPPORTPOINTS, bool UPPER>
GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	addGradGradStabilization (StackVariables const &stack, real64(&matrix)[MAXSUPPORTPOINTS NUMDOFSPERTRIALSUPPORTPOINT][MAXSUPPORTPOINTS NUMDOFSPERTRIALSUPPORTPOINT], real64 const &scaleFactor)
	Empty method, here for compatibility with methods that require a stabilization of the grad-grad bilinear form. More...

template<localIndex NUMDOFSPERTRIALSUPPORTPOINT, localIndex MAXSUPPORTPOINTS>
GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void	addEvaluatedGradGradStabilization (StackVariables const &stack, real64 const (&dofs)[MAXSUPPORTPOINTS][NUMDOFSPERTRIALSUPPORTPOINT], real64(&targetVector)[MAXSUPPORTPOINTS][NUMDOFSPERTRIALSUPPORTPOINT], real64 const scaleFactor)
	Empty method, here for compatibility with methods that require a stabilization of the grad-grad bilinear form. More...

template<int NUM_SUPPORT_POINTS>
static GEOS_HOST_DEVICE void	value (real64 const (&N)[NUM_SUPPORT_POINTS], real64 const (&var)[NUM_SUPPORT_POINTS], real64 &value)
	Compute the interpolated value of a variable. More...

template<int NUM_SUPPORT_POINTS, int NUM_COMPONENTS>
static GEOS_HOST_DEVICE void	value (real64 const (&N)[NUM_SUPPORT_POINTS], real64 const (&var)[NUM_SUPPORT_POINTS][NUM_COMPONENTS], real64(&value)[NUM_COMPONENTS])
	Compute the interpolated value of a vector variable. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	symmetricGradient (GRADIENT_TYPE const &gradN, real64 const (&var)[NUM_SUPPORT_POINTS][3], real64(&gradVar)[6])
	Calculate the symmetric gradient of a vector valued support field at a point using the stored basis function gradients for all support points. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE real64	symmetricGradientTrace (GRADIENT_TYPE const &gradN, real64 const (&var)[NUM_SUPPORT_POINTS][3])
	Calculate the trace of the symmetric gradient of a vector valued support field (i.e. the volumetric strain for the displacement field) at a point using the stored basis function gradients for all support points. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	gradient (GRADIENT_TYPE const &gradN, real64 const (&var)[NUM_SUPPORT_POINTS], real64(&gradVar)[3])
	Calculate the gradient of a scalar valued support field at a point using the input basis function gradients. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	gradient (GRADIENT_TYPE const &gradN, real64 const (&var)[NUM_SUPPORT_POINTS][3], real64(&gradVar)[3][3])
	Calculate the gradient of a vector valued support field at a point using the input basis function gradients. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	valueAndGradient (real64 const (&N)[NUM_SUPPORT_POINTS], GRADIENT_TYPE const &gradN, real64 const (&var)[NUM_SUPPORT_POINTS], real64 &value, real64(&gradVar)[3])
	Calculate the value and gradient of a scalar valued support field at a point using the input basis function gradients. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	plusGradNajAij (GRADIENT_TYPE const &gradN, real64 const (&var_detJxW)[6], real64(&R)[NUM_SUPPORT_POINTS][3])
	Inner product of each basis function gradient with a rank-2 symmetric tensor. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	plusGradNajAij (GRADIENT_TYPE const &gradN, real64 const (&var_detJxW)[3][3], real64(&R)[NUM_SUPPORT_POINTS][3])
	Inner product of each basis function gradient with a rank-2 symmetric tensor. More...

template<int NUM_SUPPORT_POINTS>
static GEOS_HOST_DEVICE void	plusNaFi (real64 const (&N)[NUM_SUPPORT_POINTS], real64 const (&forcingTerm_detJxW)[3], real64(&R)[NUM_SUPPORT_POINTS][3])
	Product of each shape function with a vector forcing term. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	plusGradNajAijPlusNaFi (GRADIENT_TYPE const &gradN, real64 const (&var_detJxW)[3][3], real64 const (&N)[NUM_SUPPORT_POINTS], real64 const (&forcingTerm_detJxW)[3], real64(&R)[NUM_SUPPORT_POINTS][3])
	Inner product of each basis function gradient with a rank-2 symmetric tensor added to the product each shape function with a vector. More...

template<int NUM_SUPPORT_POINTS, typename GRADIENT_TYPE >
static GEOS_HOST_DEVICE void	plusGradNajAijPlusNaFi (GRADIENT_TYPE const &gradN, real64 const (&var_detJxW)[6], real64 const (&N)[NUM_SUPPORT_POINTS], real64 const (&forcingTerm_detJxW)[3], real64(&R)[NUM_SUPPORT_POINTS][3])
	Inner product of each basis function gradient with a rank-2 tensor added to the product each shape function with a vector. More...

Static Public Attributes
static constexpr int	order = ORDER
	The order of the finite element.

constexpr static localIndex	numNodes = ( ORDER + 1 ) * ( ORDER + 2 ) * ( ORDER + 3 ) / 6
	The number of shape functions per element.

constexpr static localIndex	numNodesPerFace = ( ORDER + 1 ) * ( ORDER + 2 ) / 2
	The number of shape functions per face.

constexpr static localIndex	maxSupportPoints = numNodes
	The maximum number of support points per element.

constexpr static localIndex	numQuadraturePoints = numNodes
	The number of quadrature points per element.

Static Public Attributes inherited from geos::finiteElement::FiniteElementBase
constexpr static int	numSamplingPointsPerDirection = 10
	Number of sampling points.

Additional Inherited Members
Protected Attributes inherited from geos::finiteElement::FiniteElementBase
arrayView4d< real64 const >	m_viewGradN
	View to potentially hold pre-calculated shape function gradients.

arrayView2d< real64 const >	m_viewDetJ

Detailed Description

template<int ORDER>
class geos::finiteElement::BB_Tetrahedron< ORDER >

This class contains the kernel accessible functions specific to the Bernstein-Bézier (BB) modal any-order tetrahedron finite element with Gaussian quadrature rules. Available functions are tailored for Discontinuous Galerkin (DG) applications. In barycentric coordinates l1, l2, l3, l4, the function indexed by (i1, i2, i3, i4) corresponds to the function (i1+i2+i3+i4+3)! / (i1! i2! i3! i4!) l1^i1 l2^i2 l3^i3 l4^i4 and they integrate to one over the reference element defined by 0<=l1,l2,l3,l3<=1, l1+l2+l3+l4=1

Definition at line 45 of file BB_Tetrahedron.hpp.

Constructor & Destructor Documentation

◆ ~BB_Tetrahedron()

template<int ORDER>

virtual geos::finiteElement::BB_Tetrahedron< ORDER >::~BB_Tetrahedron ( )

virtualdefault

Doxygen_Suppress

Member Function Documentation

◆ barycentricCoordinateLoop()

template<int ORDER>

template<typename FUNC >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::barycentricCoordinateLoop ( FUNC && func )

inlinestaticconstexpr

Helper function for loop over barycentric coordinates.

Template Parameters

FUNC	the callback function

Parameters

func	the callback function to call for each index

Definition at line 678 of file BB_Tetrahedron.hpp.

◆ basisLoop()

template<int ORDER>

template<typename FUNC >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::basisLoop ( FUNC && func )

inlinestaticconstexpr

Helper function for loop over tet basis functions.

Template Parameters

FUNC	the callback function

Parameters

func	the callback function to call for each index

Definition at line 691 of file BB_Tetrahedron.hpp.

◆ calcGradN() [1/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::calcGradN	(	localIndex const	q,
		real64 const (&)	X[numNodes][3],
		real64(&)	gradN[numNodes][3]
	)

inlinestatic

Calculate the shape functions derivatives wrt the physical coordinates.

Parameters

q	Index of the quadrature point.
X	Array containing the coordinates of the mesh support points.
gradN	Array to contain the shape function derivatives for all support points at the coordinates of the quadrature point `q`.

Returns: The determinant of the parent/physical transformation matrix.

Definition at line 411 of file BB_Tetrahedron.hpp.

◆ calcGradN() [2/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::calcGradN	(	localIndex const	q,
		real64 const (&)	X[numNodes][3],
		StackVariables const &	stack,
		real64(&)	gradN[numNodes][3]
	)

inlinestatic

Calculate the shape functions derivatives wrt the physical coordinates.

Parameters

q	Index of the quadrature point.
X	Array containing the coordinates of the mesh support points.
stack	Variables allocated on the stack as filled by setupStack.
gradN	Array to contain the shape function derivatives for all support points at the coordinates of the quadrature point `q`.

Returns: The determinant of the parent/physical transformation matrix.

Definition at line 434 of file BB_Tetrahedron.hpp.

◆ calcN() [1/4]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcN	(	localIndex const	q,
		StackVariables const &	stack,
		real64(&)	N[numNodes]
	)

inlinestatic

Calculate shape functions values for each support point at a quadrature point.

Parameters

q	Index of the quadrature point.
stack	Variables allocated on the stack as filled by setupStack.
N	An array to pass back the shape function values for each support point.

Definition at line 194 of file BB_Tetrahedron.hpp.

◆ calcN() [2/4]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcN	(	localIndex const	,
		real64(&)	N[numNodes]
	)

inlinestatic

Calculate shape functions values for each support point at a quadrature point.

Parameters

N	An array to pass back the shape function values for each support point.

Definition at line 174 of file BB_Tetrahedron.hpp.

◆ calcN() [3/4]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcN	(	real64 const (&)	lambda[4],
		real64(&)	N[numNodes]
	)

inlinestatic

Calculate shape functions values at a single point using De Casteljau's algorithm.

Parameters

[in]	lambda	barycentric coordinates of the point in thetetrahedron
[out]	N	The shape function.

Definition at line 208 of file BB_Tetrahedron.hpp.

◆ calcN() [4/4]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcN	(	real64 const (&)	X[4][3],
		real64 const (&)	coords[3],
		real64(&)	N[numNodes]
	)

inlinestatic

Calculate shape functions values at a single point, given the coordinates of the tetrahedron vertices, using De Casteljau's algorithm.

Parameters

[in]	X	Array containing the coordinates of the support points.
[in]	coords	The parent coordinates at which to evaluate the shape function value, in the reference element
[in]	N	An array to pass back the shape function values for each support point

Definition at line 256 of file BB_Tetrahedron.hpp.

◆ calcNandGradN() [1/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcNandGradN	(	real64 const (&)	lambda[4],
		real64 const (&)	N[numNodes],
		real64(&)	gradN[numNodes][4]
	)

inlinestatic

Calculate the values and derivatives of shape functions with respect to barycentric coordinates at a single point using De Casteljau's algorithm.

Parameters

[in]	lambda	barycentric coordinates of the point in thetetrahedron
[out]	N	The shape function values.
[out]	gradN	The derivatives of the shape functions with respect to the lambdas

Definition at line 295 of file BB_Tetrahedron.hpp.

◆ calcNandGradN() [2/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::calcNandGradN	(	real64 const (&)	X[4][3],
		real64 const (&)	coords[3],
		real64(&)	N[numNodes],
		real64(&)	gradN[numNodes][4]
	)

inlinestatic

Calculate the shape functions values and derivatives at a single point, given the coorginates of the tetrahedron vertices, using De Casteljau's algorithm.

Parameters

[in]	X	An array containing the coordinates of the tetrahedra
[in]	coords	The parent coordinates at which to evaluate the shape function value, in the reference element
[in]	N	An array to pass back the shape function values for each support
[out]	gradN	The derivatives of the shape functions with respect to the lambdas

Definition at line 354 of file BB_Tetrahedron.hpp.

◆ call_matching_cases()

template<int ORDER>

template<int c1, int i1, int j1, int k1, int l1, typename F , int... Is>

static constexpr GEOS_HOST_DEVICE void geos::finiteElement::BB_Tetrahedron< ORDER >::call_matching_cases	(	F &&	func,
		std::integer_sequence< int, Is... >
	)

inlinestaticconstexpr

Helper function for loop over tet basis functions that have one index in a given set of indices. If multiple indices are in the given list, the callback is called multiple times. This herlper is useful to avoid too much fold operations.

Template Parameters

c1	the dof index in the element
i1	the index with respect to the first vertex
j1	the index with respect to the second vertex
k1	the index with respect to the third vertex
l1	the index with respect to the fourth vertex
F	the callback function type
Is	the set of indices to check against

Parameters

func	the callback function to call for each matching index

Definition at line 739 of file BB_Tetrahedron.hpp.

◆ computeFaceSuperpositionIntegral()

template<int ORDER>

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::computeFaceSuperpositionIntegral	(	const int	i1,
		const int	j1,
		const int	k1,
		const int	i2,
		const int	j2,
		const int	k2
	)

inlinestaticconstexpr

Computes the superposition integral over a face between Bernstein-Bézier functions whose indices are given by (i1, j1, k1, l1=0 ) and (i1, j2, k2, l2=0)

Parameters

[in]	i1
[in]	j1
[in]	k1
[in]	i2
[in]	j2
[in]	k2

Returns: the superposition integral over the barycentric coordinates

Definition at line 536 of file BB_Tetrahedron.hpp.

◆ computeFluxDerivativeFactor()

template<int ORDER>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::computeFluxDerivativeFactor	(	real64 const (&)	X[4][3],
		int	x1,
		int	x2,
		int	o1,
		int	o2
	)

inlinestaticconstexpr

Function to compute the factor for the flux derivative term.

Parameters

X	Array containing the coordinates of the support points.
x1	Index of the first edge vertex
x2	Index of the second edge vertex
o1	Index of the first face vertex
o2	Index of the second face vertex

Returns: The factor for the flux derivative term

Definition at line 1127 of file BB_Tetrahedron.hpp.

◆ computeMassTerm()

template<int ORDER>

template<typename FUNC >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::computeMassTerm	(	real64 const (&)	X[4][3],
		FUNC &&	func
	)

inlinestaticconstexpr

Computes the non-zero contributions inside the element of the mass matrix M, i.e., the superposition matrix of shape functions.

Parameters

X	Array containing the coordinates of the support points.
func	Callback function accepting three parameters: i, j (local d.o.f. inside the element) and M_ij

Definition at line 1068 of file BB_Tetrahedron.hpp.

◆ computeReferenceDampingMatrix()

template<int ORDER>

template<typename DAMPING >

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::computeReferenceDampingMatrix	(	real64(&)	d[numNodes][numNodes],
		bool const	face1Damped,
		bool const	face2Damped,
		bool const	face3Damped,
		bool const	face4Damped
	)

inlinestatic

Computes the reference damping matrix, i.e., the superposition matrix of the shape functions in barycentric coordinates over faces. The real-world mass matrix can be obtained by using the multiplying this matrix by the determinant of the face Jacobian.

Parameters

[out]	d	The damping matrix
[in]	face1Damped	Whether the first face contributes to the damping term
[in]	face2Damped	Whether the second face contributes to the damping term
[in]	face3Damped	Whether the third face contributes to the damping term
[in]	face4Damped	Whether the fourth face contributes to the damping term

Definition at line 1027 of file BB_Tetrahedron.hpp.

◆ computeReferenceMassMatrix()

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::computeReferenceMassMatrix ( arraySlice2d< real64 > const & m )

inlinestatic

Computes the reference mass matrix, i.e., the superposition matrix of the shape functions in barycentric coordinates. The real-world mass matrix can be obtained by using the multiplying this matrix by the determinant of the Jacobian.

Parameters

[out] m The mass matrix

Definition at line 987 of file BB_Tetrahedron.hpp.

◆ computeStiffnessTerm()

template<int ORDER>

template<typename FUNC >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::computeStiffnessTerm	(	real64 const (&)	X[4][3],
		FUNC &&	func
	)

inlinestaticconstexpr

Computes the non-zero contributions inside the element of the stiffness matrix R, i.e., the superposition matrix of first derivatives of shape functions.

Parameters

X	Array containing the coordinates of the support points.
func	Callback function accepting three parameters: i, j (local d.o.f. inside the element) and R_ij

Definition at line 1175 of file BB_Tetrahedron.hpp.

◆ computeSuperpositionIntegral()

template<int ORDER>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::computeSuperpositionIntegral	(	const int	i1,
		const int	j1,
		const int	k1,
		const int	l1,
		const int	i2,
		const int	j2,
		const int	k2,
		const int	l2
	)

inlinestaticconstexpr

Computes the superposition integral between Bernstein-Bézier functions indexed by (i1, j1, k1, l1) and (i1, j2, k2, l2)

Parameters

[in]	i1
[in]	j1
[in]	k1
[in]	l1
[in]	i2
[in]	j2
[in]	k2
[in]	l2

Returns: the superposition integral over the barycentric coordinates

Definition at line 512 of file BB_Tetrahedron.hpp.

◆ computeSurfaceTerms()

template<int ORDER>

template<typename FUNCP , typename FUNCF >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::computeSurfaceTerms	(	real64 const (&)	X[4][3],
		FUNCP &&	funcP,
		FUNCF &&	funcF
	)

inlinestaticconstexpr

Computes the non-zero contributions inside the element of the surface terms, including the value of the superposition integral of basis functions (used for the penalty and damping terms) and the superposition integral of the derivative of a function with the value of the other, used for the flux terms.

Parameters

X	Array containing the coordinates of the support points.
funcP	Callback function for non-zero penalty-type terms, accepting seven parameters: c1, c2 (local d.o.f. inside the element), f (index of the face, i.e., index of the opposite vertex for this element), i1, j1 and k1 (local indices for the first shape function) and value i2, j2 and k2 (local indices for the second shape function) and value
funcF	Callback function for non-zero flux-type terms, accepting four parameters: c2, c2 (local d.o.f. inside the element), f (index of the face, i.e., index of the opposite vertex for this element), and value i1, j1 and k1 (local indices for the first shape function) and value i2, j2 and k2 (local indices for the second shape function) and value

Definition at line 1277 of file BB_Tetrahedron.hpp.

◆ conditionalBasisLoop()

template<int ORDER>

template<int... Is, typename FUNC >

static constexpr GEOS_HOST_DEVICE void geos::finiteElement::BB_Tetrahedron< ORDER >::conditionalBasisLoop ( FUNC const & func )

inlinestaticconstexpr

Helper function for loop over tet basis functions that have one index in a given set of indices. If multiple indices are in the given list, the callback is called multiple times.

Template Parameters

FUNC	the callback function
Is	the setindices

Parameters

func	the callback function to call for each index

Definition at line 801 of file BB_Tetrahedron.hpp.

◆ correctionFactorDerivative()

template<int ORDER>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::correctionFactorDerivative	(	int const	i1,
		int const	j1,
		int const	k1,
		int const	l1,
		int const	i2,
		int const	j2,
		int const	k2,
		int const	l2,
		int const	dim
	)

inlinestaticconstexpr

Computes the correction factor for the superposition integral in case a function has been derived once. The indices of the original function are ii1, j1, k1 and l1, and those of the once-derived one are i2, j2, k2 and l2.

Parameters

[in]	i1
[in]	j1
[in]	k1
[in]	l1
[in]	i2
[in]	j2
[in]	k2
[in]	l2
[in]	dim	the dimension, 2 or 3

Returns: the correction factor to be applied to the superposition integral

Definition at line 491 of file BB_Tetrahedron.hpp.

◆ dofIndex() [1/2]

template<int ORDER>

template<int I, int J, int K>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int geos::finiteElement::BB_Tetrahedron< ORDER >::dofIndex ( )

inlinestaticconstexpr

Computes the local degree of freedom index given the shape function indices (i, j, k, l) for each vertex. Only i, j and k are needed since i + j + k + l = order.

Template Parameters

I	The index with respect to the first vertex
J	The index with respect to the second vertex
K	The index with respect to the third vertex

Returns: The local degree of freedom index

Definition at line 561 of file BB_Tetrahedron.hpp.

◆ dofIndex() [2/2]

template<int ORDER>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int geos::finiteElement::BB_Tetrahedron< ORDER >::dofIndex	(	const int	i,
		const int	j,
		const int	k
	)

inlinestaticconstexpr

Computes the local degree of freedom index given the shape function indices (i, j, k, l) for each vertex. Only i, j and k are needed since i + j + k + l = order This version takes indices as parameters and can be called with non-constexpr index values.

Parameters

i	The index with respect to the first vertex
j	The index with respect to the second vertex
k	The index with respect to the third vertex

Returns: The local degree of freedom index

Definition at line 582 of file BB_Tetrahedron.hpp.

◆ edgeLength2()

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::edgeLength2	(	localIndex	i1,
		localIndex	i2,
		real64 const (&)	X[4][3]
	)

inlinestatic

Compute th length of the edge between two vertices i1 and i2

Parameters

i1	Index of the first vertex
i2	Index of the second vertex
X	Array containing the coordinates of the support points.

Returns: The squared length of the edge between the two vertices

Definition at line 1247 of file BB_Tetrahedron.hpp.

◆ faceBarycentricCoordinateLoop()

template<int ORDER>

template<typename FUNC >

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::faceBarycentricCoordinateLoop ( FUNC && func )

inlinestaticconstexpr

Helper function for loop over barycentric coordinates of a face.

Template Parameters

FUNC	the callback function

Parameters

func	the callback function to call for each index

Definition at line 971 of file BB_Tetrahedron.hpp.

◆ faceJacobianDeterminant()

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::faceJacobianDeterminant	(	localIndex	face,
		real64 const (&)	X[4][3]
	)

inlinestatic

Calculate the determinant of the jacobian on the face opposite to the given vertex.

Parameters

[in]	face	The index of the vertex opposite to the desired face
[in]	X	The coordinates of the tetrahedron

Returns: the (absolute value of the) determinant of the Jacobian on the face

Definition at line 146 of file BB_Tetrahedron.hpp.

◆ getMaxSupportPoints()

template<int ORDER>

GEOS_HOST_DEVICE virtual GEOS_FORCE_INLINE localIndex geos::finiteElement::BB_Tetrahedron< ORDER >::getMaxSupportPoints ( ) const

inlineoverridevirtual

Get the maximum number of support points for this element.

This should be used to know the size of pre-allocated objects whose size depend on the number of support points.

Returns: The number of maximum support points for this element.

Implements geos::finiteElement::FiniteElementBase.

Definition at line 98 of file BB_Tetrahedron.hpp.

◆ getNumQuadraturePoints() [1/2]

template<int ORDER>

virtual GEOS_HOST_DEVICE localIndex geos::finiteElement::BB_Tetrahedron< ORDER >::getNumQuadraturePoints ( ) const

inlineoverridevirtual

Virtual getter for the number of quadrature points per element.

Returns: The number of quadrature points per element.

Implements geos::finiteElement::FiniteElementBase.

Definition at line 71 of file BB_Tetrahedron.hpp.

◆ getNumQuadraturePoints() [2/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE localIndex geos::finiteElement::BB_Tetrahedron< ORDER >::getNumQuadraturePoints ( StackVariables const & stack )

inlinestatic

Get the number of quadrature points.

Parameters

stack Stack variables as filled by setupStack.

Returns: The number of quadrature points.

Definition at line 83 of file BB_Tetrahedron.hpp.

◆ getNumSupportPoints() [1/2]

template<int ORDER>

GEOS_HOST_DEVICE virtual GEOS_FORCE_INLINE localIndex geos::finiteElement::BB_Tetrahedron< ORDER >::getNumSupportPoints ( ) const

inlineoverridevirtual

Virtual getter for the number of support points per element.

Returns: The number of support points per element.

Implements geos::finiteElement::FiniteElementBase.

Definition at line 91 of file BB_Tetrahedron.hpp.

◆ getNumSupportPoints() [2/2]

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE localIndex geos::finiteElement::BB_Tetrahedron< ORDER >::getNumSupportPoints ( StackVariables const & stack )

inlinestatic

Get the number of support points.

Parameters

stack Object that holds stack variables.

Returns: The number of support points.

Definition at line 110 of file BB_Tetrahedron.hpp.

◆ indexToIJKL()

template<int ORDER>

template<int C, int VTX>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE int geos::finiteElement::BB_Tetrahedron< ORDER >::indexToIJKL ( )

inlinestaticconstexpr

Computes the local degree of freedom index given the shape function indices for each vertex.

Template Parameters

C	The dof index in the element
VTX	the vertex with respect to

Returns: i, j, k, l if VTX= 0, 1, 2 or 3 resepctively (with i + j + k + l = order)

Definition at line 603 of file BB_Tetrahedron.hpp.

◆ integralTerm()

template<int ORDER>

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::integralTerm	(	const int	a,
		const int	b,
		const int	c
	)

inlinestaticconstexpr

Computes a! / ( b! * c! ) with b + c >= a >= b, c.

Parameters

[in]	a
[in]	b
[in]	c

Returns: a!/(b!*c!)

Definition at line 452 of file BB_Tetrahedron.hpp.

◆ jacobianDeterminant()

template<int ORDER>

GEOS_HOST_DEVICE static GEOS_FORCE_INLINE real64 geos::finiteElement::BB_Tetrahedron< ORDER >::jacobianDeterminant ( real64 const (&) X[4][3] )

inlinestatic

Returns the determinant of the Jacobian of the element.

Parameters

[in] X The coordinates of the tetrahedron

Returns: the (absolute value of the) determinant of the Jacobian on the element

Definition at line 124 of file BB_Tetrahedron.hpp.

◆ loop()

template<int ORDER>

template<int N, typename FUNC >

static constexpr GEOS_HOST_DEVICE void geos::finiteElement::BB_Tetrahedron< ORDER >::loop ( FUNC const & func )

inlinestaticconstexpr

Helper function for static for loop.

Template Parameters

N	the number of iterations
FUNC	the callback function

Parameters

func	the callback function to call for each index This function recursively calls itself until N reaches 0, at which point it stops.

Definition at line 659 of file BB_Tetrahedron.hpp.

◆ loop_impl()

template<int ORDER>

template<typename FUNC , int... Is>

GEOS_HOST_DEVICE static constexpr GEOS_FORCE_INLINE void geos::finiteElement::BB_Tetrahedron< ORDER >::loop_impl	(	FUNC &&	func,
		std::integer_sequence< int, Is... >
	)

inlinestaticconstexpr

Helper function for static for loop.

Template Parameters

FUNC	the callback function
...Is	integer indices of the loop

Parameters

func	the callback function to call for each index

Template Parameters

Is	the integer indices of the loop

Definition at line 645 of file BB_Tetrahedron.hpp.

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

coreComponents/finiteElement/elementFormulations/BB_Tetrahedron.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

template<int ORDER> class geos::finiteElement::BB_Tetrahedron< ORDER >

Constructor & Destructor Documentation

◆ ~BB_Tetrahedron()

Member Function Documentation

◆ barycentricCoordinateLoop()

◆ basisLoop()

◆ calcGradN() [1/2]

◆ calcGradN() [2/2]

◆ calcN() [1/4]

◆ calcN() [2/4]

◆ calcN() [3/4]

◆ calcN() [4/4]

◆ calcNandGradN() [1/2]

◆ calcNandGradN() [2/2]

◆ call_matching_cases()

◆ computeFaceSuperpositionIntegral()

◆ computeFluxDerivativeFactor()

◆ computeMassTerm()

◆ computeReferenceDampingMatrix()

◆ computeReferenceMassMatrix()

◆ computeStiffnessTerm()

◆ computeSuperpositionIntegral()

◆ computeSurfaceTerms()

◆ conditionalBasisLoop()

◆ correctionFactorDerivative()

◆ dofIndex() [1/2]

◆ dofIndex() [2/2]

◆ edgeLength2()

◆ faceBarycentricCoordinateLoop()

◆ faceJacobianDeterminant()

◆ getMaxSupportPoints()

◆ getNumQuadraturePoints() [1/2]

◆ getNumQuadraturePoints() [2/2]

◆ getNumSupportPoints() [1/2]

◆ getNumSupportPoints() [2/2]

◆ indexToIJKL()

◆ integralTerm()

◆ jacobianDeterminant()

◆ loop()

◆ loop_impl()

template<int ORDER>
class geos::finiteElement::BB_Tetrahedron< ORDER >