#include <karniadakis.hh>

Inheritance diagram for concepts::Karniadakis< type, mode >:

Public Member Functions
	Karniadakis (const int P, const Real *xP, const int NxP, const int Q=0, const int R=0, const bool cache=true)

	Karniadakis (const int P, int NxP, const Real *values, const int Q=0, const int R=0)

	Karniadakis (const Karniadakis< type, mode > &arg)
	Copy constructor.

uint	n () const
	Returns the number of shape functions.

uint	nP () const

const Real *	values () const
	Returns the values of the shape functions.

Static Public Member Functions
static void	clearCache ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Protected Attributes
Real *	values_
	Values of the shape functions.

Detailed Description

template<int type, int mode>
class concepts::Karniadakis< type, mode >

Part of the multidimensional expansion bases for the shape functions of Karniadakis and Sherwin. Computes one of principal functions $\psi^a_i(z)$ , $\psi^b_{ij}(z)$ or $\psi^c_{ijk}(z)$ for given polynomial degrees and a set of points.

The constructor computes the values if necessary: they are stored in static hashes and can be reused if requested a second time. There is a method to get a pointer into the array of the computed values, use this at initialization time of the element to get a pointer to the values. The index of the points in which the shape functions are evaluated runs fastest, k is second and i is slowest.

Parameters

type

Template parameter: type of the principal function. Can take the values

1 – The principal function $\psi^a_i(z)$ is computed in the constructor.
2 – The principal function $\psi^b_{ij}(z)$ is computed in the constructor.
3 – The principal function $\psi^c_{ijk}(z)$ is computed in the constructor.

mode

Template parameter: normal, derivatives, divided form. Can take the values

0 – normal
1 – derivatives. The derivatives of principal function are computed in the constructor, ie. ${\psi^a_i}'(z)$ , ${\psi^b_{ij}}'(z)$ and ${\psi^c_{ijk}}'(z)$ respectively, depending on the type of the principal function
2 – divided form. The principal function is divided by : $\frac{\psi^b_{ij}(z)}{1-z}$ is computed in the constructor. This is only possible for the principal function $\psi^b_{ij}(z)$ .

Test:: test::KarniadakisTest

Author: Philipp Frauenfelder, 2000

Definition at line 163 of file karniadakis.hh.

Constructor & Destructor Documentation

◆ Karniadakis() [1/2]

template<int type, int mode>

concepts::Karniadakis< type, mode >::Karniadakis	(	const int	P,
		const Real *	xP,
		const int	NxP,
		const int	Q = `0`,
		const int	R = `0`,
		const bool	cache = `true`
	)

Constructor. Computes the values of the principal function of the given order and in the given points.

(P+1)*(Q+1)*(R+1) is the number of shape functions which have to be computed in NxP points.

Parameters

P	Order of the principal function in $\eta_1$
xP	Points
NxP	Number of points
Q	Order of the principal function in $\eta_2$
R	Order of the principal function in $\eta_3$
cache	Controls if the computed values should be taken from and stored in the cache

◆ Karniadakis() [2/2]

template<int type, int mode>

concepts::Karniadakis< type, mode >::Karniadakis	(	const int	P,
		int	NxP,
		const Real *	values,
		const int	Q = `0`,
		const int	R = `0`
	)

Value copy constructor. Copies precomputed values for the karniadakis polynomials to its value data. The chache is setted false since, the values data will be allocated.

Parameters

P	Order of the principal function in $\eta_1$
NxP	Number of quadratur points
values	precomputed values
Q	Order of the principal function in $\eta_2$
R	Order of the principal function in $\eta_3$
cache	Controls if the computed values should be taken from and stored in the cache

Member Function Documentation

◆ clearCache()

template<int type, int mode>

static void concepts::Karniadakis< type, mode >::clearCache ( )

inlinestatic

Definition at line 204 of file karniadakis.hh.

◆ info()

template<int type, int mode>

virtual std::ostream & concepts::Karniadakis< type, mode >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Implements concepts::ShapeFunction1D< Real >.

◆ n()

uint concepts::ShapeFunction1D< Real >::n ( ) const

inlineinherited

Returns the number of shape functions.

Definition at line 35 of file shapefunction.hh.

◆ nP()

uint concepts::ShapeFunction1D< Real >::nP ( ) const

inlineinherited

Returns the number of abscissas (in which the shape functions are evaluated)

Definition at line 38 of file shapefunction.hh.

◆ values()

const Real * concepts::ShapeFunction1D< Real >::values ( ) const

inlineinherited

Returns the values of the shape functions.

Definition at line 40 of file shapefunction.hh.

Member Data Documentation

◆ values_

Real * concepts::ShapeFunction1D< Real >::values_

protectedinherited

Values of the shape functions.

Definition at line 45 of file shapefunction.hh.

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

integration/karniadakis.hh

Class documentation of Concepts

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Karniadakis() [1/2]

◆ Karniadakis() [2/2]

Member Function Documentation

◆ clearCache()

◆ info()

◆ n()

◆ nP()

◆ values()

Member Data Documentation

◆ values_