The ShapeFunction class defines the shape functions, \( N(\xi)^e \), for a given reference element \( \overline{\Omega^e} \). More...

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

Inheritance diagram for axom::mint::ShapeFunction< ShapeType >:

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Static Public Member Functions
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<typename ShapeType>
class axom::mint::ShapeFunction< ShapeType >

The ShapeFunction class defines the shape functions, \( N(\xi)^e \), for a given reference element \( \overline{\Omega^e} \).

ShapeFunction is a templated class that employs the Curiously Recurring Template Pattern (CRTP) to provide a unified API for all underlying ShapeFunction implementations.

See also: FiniteElement; FEBasisTypes.hpp

Member Function Documentation

◆ cellType()

template<typename ShapeType >

static CellType axom::mint::ShapeFunction< ShapeType >::cellType ( )

inlinestatic

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

Returns: cellType the cell type

See also: CellType.hpp

◆ type()

template<typename ShapeType >

static int axom::mint::ShapeFunction< ShapeType >::type ( )

inlinestatic

Returns the Finite Element basis family type.

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

See also: FEBasisTypes.hpp

◆ numDofs()

template<typename ShapeType >

static int axom::mint::ShapeFunction< ShapeType >::numDofs ( )

inlinestatic

Returns the number of degrees of freedom.

Returns: ndofs the number of degrees of freedom

Postcondition: ndofs >= 1

◆ maxNewtonIters()

template<typename ShapeType >

static int axom::mint::ShapeFunction< ShapeType >::maxNewtonIters ( )

inlinestatic

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

Returns: N the maximum number of Newton-Raphson iterations

◆ dimension()

template<typename ShapeType >

static int axom::mint::ShapeFunction< ShapeType >::dimension ( )

inlinestatic

Returns the dimension of the reference element.

Returns: ndims the dimension of the reference element

Postcondition: ndims >= 1

◆ min()

template<typename ShapeType >

static double axom::mint::ShapeFunction< ShapeType >::min ( )

inlinestatic

Returns the min coordinate of the reference element.

Returns: min the min coordinate of the reference element

◆ max()

template<typename ShapeType >

static double axom::mint::ShapeFunction< ShapeType >::max ( )

inlinestatic

Returns the max coordinate of the reference element.

Returns: max the max coordinate of the reference element

◆ center()

template<typename ShapeType >

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

inlinestatic

Returns the center of the reference element.

Parameters

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

Precondition: center != nullptr

◆ coords()

template<typename ShapeType >

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

inlinestatic

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()

template<typename ShapeType >

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

inlinestatic

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()

template<typename ShapeType >

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

inlinestatic

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/latest/src/axom/mint/fem/shape_functions/ShapeFunction.hpp

Static Public Member Functions

Detailed Description

template<typename ShapeType> class axom::mint::ShapeFunction< ShapeType >

Member Function Documentation

◆ cellType()

◆ type()

◆ numDofs()

◆ maxNewtonIters()

◆ dimension()

◆ min()

◆ max()

◆ center()

◆ coords()

◆ evaluate()

◆ derivatives()

template<typename ShapeType>
class axom::mint::ShapeFunction< ShapeType >