Defines the Lagrange family of Finite Elements. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/mint/fem/shape_functions/Lagrange.hpp>

Inheritance diagram for axom::mint::Lagrange< CELLTYPE >:

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Static Public Member Functions
static CellType	getCellType ()
	Returns the cell type of this instance. More...

static int	getType ()
	Returns the Basis function type. More...

static int	getNumDofs ()
	Returns the number of degrees of freedom on this Finite Element. More...

static int	getMaxNewtonIters ()
	Returns the max number of newton iterations for this Finite Element. More...

static int	getDimension ()
	Returns the dimension of the reference element. More...

static int	getMin ()
	Returns the min coordinate of the element's reference space. More...

static int	getMax ()
	Returns the max coordinate of the element's reference space. More...

static void	getCenter (double *AXOM_UNUSED_PARAM(center))
	Returns the centroid of the reference element. More...

static void	getCoords (double *AXOM_UNUSED_PARAM(coords))
	Returns the coordinates of the reference element. More...

static void	computeShape (const double AXOM_UNUSED_PARAM(nc), double AXOM_UNUSED_PARAM(phi))
	Computes the shape functions of the Finite Element at the given natural coordinates, \( \xi \). More...

static void	computeDerivatives (const double AXOM_UNUSED_PARAM(nc), double AXOM_UNUSED_PARAM(phidot))
	Computes the shape function first derivatives for the Finite Element at the given natural coordinates, \( \xi \). More...

Generic ShapeFunction API
static CellType	cellType ()
	Returns the underlying cell type, e.g., MINT_QUAD, etc. More...

static int	type ()
	Returns the Finite Element basis family type. More...

static int	numDofs ()
	Returns the number of degrees of freedom. More...

static int	maxNewtonIters ()
	Returns the maximum number of iterations for the Newton-Raphson. More...

static int	dimension ()
	Returns the dimension of the reference element. More...

static double	min ()
	Returns the min coordinate of the reference element. More...

static double	max ()
	Returns the max coordinate of the reference element. More...

static void	center (double *center)
	Returns the center of the reference element. More...

static void	coords (double *coords)
	Returns the coordinates of the reference element. More...

static void	evaluate (const double nc, double phi)
	Evaluates the ShapeFunction at the given natural coordinates. More...

static void	derivatives (const double nc, double phidot)
	Evaluates the first derivatives of the shape function at the given natural coordinates. More...

Detailed Description

template<CellType CELLTYPE>
class axom::mint::Lagrange< CELLTYPE >

Defines the Lagrange family of Finite Elements.

Template Parameters

CELLTYPE the cell type of the element, e.g., mint::QUAD, etc.

Note: This is the default implementation. Only stubs are defined at this level.This class is specialized according to cell type.

Member Function Documentation

◆ getCellType()

template<CellType CELLTYPE>

static CellType axom::mint::Lagrange< CELLTYPE >::getCellType ( )

inlinestatic

Returns the cell type of this instance.

Returns: c the cell type, e.g., MINT_QUAD etc.

See also: CellTypes.hpp

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getType()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getType ( )

inlinestatic

Returns the Basis function type.

Returns: b the basis thpe, e.g., MINT_LAGRANGE_BASIS

See also: FEBasisTypes.hpp

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), MINT_UNDEFINED_BASIS, and axom::mint::NUM_CELL_TYPES.

◆ getNumDofs()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getNumDofs ( )

inlinestatic

Returns the number of degrees of freedom on this Finite Element.

Returns: nodfs the number of degrees of freedom.

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getMaxNewtonIters()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getMaxNewtonIters ( )

inlinestatic

Returns the max number of newton iterations for this Finite Element.

Returns: N the max number of newton iterations

Postcondition: N >= 1

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getDimension()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getDimension ( )

inlinestatic

Returns the dimension of the reference element.

Returns: dim the dimension of the reference element

Postcondition: dim >= 1 && dim <= 3

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getMin()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getMin ( )

inlinestatic

Returns the min coordinate of the element's reference space.

Returns: min the min coordinate of the element's reference space, e.g., 0

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getMax()

template<CellType CELLTYPE>

static int axom::mint::Lagrange< CELLTYPE >::getMax ( )

inlinestatic

Returns the max coordinate of the element's reference space.

Returns: max the max coordinate of the element's reference space, e.g., 1

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getCenter()

template<CellType CELLTYPE>

static void axom::mint::Lagrange< CELLTYPE >::getCenter ( double * AXOM_UNUSED_PARAMcenter )

inlinestatic

Returns the centroid of the reference element.

Parameters

[out] center ndims long buffer to store the centroid

Precondition: center != nullptr

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ getCoords()

template<CellType CELLTYPE>

static void axom::mint::Lagrange< CELLTYPE >::getCoords ( double * AXOM_UNUSED_PARAMcoords )

inlinestatic

Returns the coordinates of the reference element.

Parameters

[out] coords ndims*ndofs long buffer to store the coordinates

Precondition: coords != nullptr

Note: The coordinates are arranged in column-major flat array layout.; This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ computeShape()

template<CellType CELLTYPE>

static void axom::mint::Lagrange< CELLTYPE >::computeShape	(	const double *	AXOM_UNUSED_PARAMnc,
		double *	AXOM_UNUSED_PARAMphi
	)

inlinestatic

Computes the shape functions of the Finite Element at the given natural coordinates, \( \xi \).

Parameters

[in]	nc	natural coordinates at which to compute the shape functions
[out]	phi	buffer (ndofs long) to store the shape functions

Precondition: nc != nullptr; phi != nullptr

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ computeDerivatives()

template<CellType CELLTYPE>

static void axom::mint::Lagrange< CELLTYPE >::computeDerivatives	(	const double *	AXOM_UNUSED_PARAMnc,
		double *	AXOM_UNUSED_PARAMphidot
	)

inlinestatic

Computes the shape function first derivatives for the Finite Element at the given natural coordinates, \( \xi \).

Parameters

[in]	nc	natural coordinates at which to compute the derivatives
[out]	phidot	buffer (ndofs*ndims long) for the derivatives

Precondition: nc != nullptr; phidot != nullptr

Note: This method is implemented in specialized instances.

References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.

◆ cellType()

static CellType axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::cellType ( )

inlinestaticinherited

Returns the underlying cell type, e.g., MINT_QUAD, etc.

Returns: cellType the cell type

See also: CellType.hpp

◆ type()

static int axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::type ( )

inlinestaticinherited

Returns the Finite Element basis family type.

Returns: type the basis function type, e.g., MINT_LAGRANGE_BASIS

See also: FEBasisTypes.hpp

◆ numDofs()

static int axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::numDofs ( )

inlinestaticinherited

Returns the number of degrees of freedom.

Returns: ndofs the number of degrees of freedom

Postcondition: ndofs >= 1

◆ maxNewtonIters()

static int axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::maxNewtonIters ( )

inlinestaticinherited

Returns the maximum number of iterations for the Newton-Raphson.

Returns: N the maximum number of Newton-Raphson iterations

◆ dimension()

static int axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::dimension ( )

inlinestaticinherited

Returns the dimension of the reference element.

Returns: ndims the dimension of the reference element

Postcondition: ndims >= 1

◆ min()

static double axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::min ( )

inlinestaticinherited

Returns the min coordinate of the reference element.

Returns: min the min coordinate of the reference element

◆ max()

static double axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::max ( )

inlinestaticinherited

Returns the max coordinate of the reference element.

Returns: max the max coordinate of the reference element

◆ center()

static void axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::center ( double * center )

inlinestaticinherited

Returns the center of the reference element.

Parameters

[out] center buffer (ndims long) to store the centroid

Precondition: center != nullptr

◆ coords()

static void axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::coords ( double * coords )

inlinestaticinherited

Returns the coordinates of the reference element.

Parameters

[out] coords buffer (ndims*ndofs long) to store the coordinates

Precondition: coords != nullptr

Note: THe coordinates are arranged in column-major flat array layout

◆ evaluate()

static void axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::evaluate	(	const double *	nc,
		double *	phi
	)

inlinestaticinherited

Evaluates the ShapeFunction at the given natural coordinates.

Parameters

[in]	nc	natural coordinates at which to compute the shape functions
[out]	phi	buffer (ndofs long) to store the shape function.

Precondition: nc != nullptr; phi != nullptr

◆ derivatives()

static void axom::mint::ShapeFunction< Lagrange< CELLTYPE > >::derivatives	(	const double *	nc,
		double *	phidot
	)

inlinestaticinherited

Evaluates the first derivatives of the shape function at the given natural coordinates.

Parameters

[in]	nc	natural coordinates at which to compute the derivatives
[out]	phidot	buffer (ndofs*ndims long) to store the derivatives

Precondition: nc != nullptr; phidot != nullptr

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/mint/fem/shape_functions/Lagrange.hpp

Static Public Member Functions

Detailed Description

template<CellType CELLTYPE> class axom::mint::Lagrange< CELLTYPE >

Member Function Documentation

◆ getCellType()

◆ getType()

◆ getNumDofs()

◆ getMaxNewtonIters()

◆ getDimension()

◆ getMin()

◆ getMax()

◆ getCenter()

◆ getCoords()

◆ computeShape()

◆ computeDerivatives()

◆ cellType()

◆ type()

◆ numDofs()

◆ maxNewtonIters()

◆ dimension()

◆ min()

◆ max()

◆ center()

◆ coords()

◆ evaluate()

◆ derivatives()

template<CellType CELLTYPE>
class axom::mint::Lagrange< CELLTYPE >