Part of the multidimensional expansion bases for the shape functions of Karniadakis and Sherwin. More...

#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)
	Constructor. More...

	Karniadakis (const int P, int NxP, const Real *values, const int Q=0, const int R=0)
	Value copy constructor. More...

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

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

uint	nP () const
	Returns the number of abscissas (in which the shape functions are evaluated) More...

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

	~Karniadakis ()

Static Public Member Functions
static void	clearCache ()

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

Protected Attributes
Real *	values_
	Values of the shape functions. More...

Private Attributes
bool	cache_
	Cache the results of the computations in principal_H if set to true. More...

uint	n_
	Number of shape functions. More...

uint	nP_
	Number of points in which the shape functions are evaluated. More...

Orders< type >	orders_
	Combines polynomial degrees and number of quadrature points. More...

Static Private Attributes
static std::unordered_map< Orders< type >, Real *, std::hash< Orders< type > >, std::OrdersEqual< type > >	principal_H
	Hash of the already computed values of the principal function of this type. More...

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() [1/3]

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() [2/3]

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

◆ Karniadakis() [3/3]

template<int type, int mode>

concepts::Karniadakis< type, mode >::Karniadakis ( const Karniadakis< type, mode > & arg )

Copy constructor.

◆ ~Karniadakis()

template<int type, int mode>

concepts::Karniadakis< type, mode >::~Karniadakis ( )

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

inlineinherited

Returns the number of shape functions.

Definition at line 35 of file shapefunction.hh.

◆ nP()

uint concepts::ShapeFunction1D< Real >::nP

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

inlineinherited

Returns the values of the shape functions.

Definition at line 40 of file shapefunction.hh.

Member Data Documentation

◆ cache_

template<int type, int mode>

bool concepts::Karniadakis< type, mode >::cache_

private

Cache the results of the computations in principal_H if set to true.

Definition at line 222 of file karniadakis.hh.

◆ n_

uint concepts::ShapeFunction1D< Real >::n_

privateinherited

Number of shape functions.

Definition at line 48 of file shapefunction.hh.

◆ nP_

uint concepts::ShapeFunction1D< Real >::nP_

privateinherited

Number of points in which the shape functions are evaluated.

Definition at line 51 of file shapefunction.hh.

◆ orders_

template<int type, int mode>

Orders<type> concepts::Karniadakis< type, mode >::orders_

private

Combines polynomial degrees and number of quadrature points.

Definition at line 211 of file karniadakis.hh.

◆ principal_H

template<int type, int mode>

std::unordered_map<Orders<type>, Real*, std::hash<Orders<type> >, std::OrdersEqual<type> > concepts::Karniadakis< type, mode >::principal_H

staticprivate

Hash of the already computed values of the principal function of this type.

The hash is static, ie. the data is available to all instances of this class.

Definition at line 219 of file karniadakis.hh.

◆ 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

concepts::Karniadakis< type, mode > Class Template Reference

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Static Private Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ Karniadakis() [1/3]

◆ Karniadakis() [2/3]

◆ Karniadakis() [3/3]

◆ ~Karniadakis()

Member Function Documentation

◆ clearCache()

◆ info()

◆ n()

◆ nP()

◆ values()

Member Data Documentation

◆ cache_

◆ n_

◆ nP_

◆ orders_

◆ principal_H

◆ values_

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