gsField< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsField< T >

A scalar of vector field defined on a m_parametric geometry.

A gsField is, generally speaking, some mathematical function that is defined on a domain of interest (the name "field" is motivated by, e.g., "scalar field" or "vector field").

The gsField combines the following:

• Geometric information on the domain:
  The domain can be represented as one single patch or as a collection of multiple patches (a.k.a. subdomains).
  This information is stored in a member of the gsMultiPatch class.
  
• The function defined on the domain:
  For each patch (a.k.a. subdomain), the gsField contains a member of class gsFunction (which represents the "local field", so to say). On this, the operations of gsFunction can be carried out (e.g., function evaluation or computation of derivatives).
  Remark: The collection of patch-wise gsFunction is stored in the private member gsField::m_fields.

Note that the geometry representation of a single patch can be extracted by calling the member function gsField::patch.

The "local field" on a single patch can be extracted by calling gsField::function.

Public Member Functions
const gsMatrix< T > &	coefficientVector (int i=0) const
	Returns the coefficient vector (if it exists) corresponding to the function field for patch i. More...
short_t	dim () const
	Returns the dimension of the physical domain (e.g., if the domain is a surface in three-dimensional space, it returns 3).
T	distanceDG (gsFunctionSet< T > const &func, bool isFunc_param=false, int=1000) const
T	distanceH1 (gsFunctionSet< T > const &func, bool isFunc_param=false, int=1000) const
T	distanceH1 (gsFunctionSet< T > const &func, gsMultiBasis< T > const &B, bool isFunc_param=false, int=1000) const
T	distanceH2 (gsFunctionSet< T > const &func, bool isFunc_param=false) const
T	distanceL2 (gsField< T > const &field, int numEvals=1000) const
	Computes the L2-distance between the two fields, on the physical domain.
T	distanceL2 (gsFunctionSet< T > const &func, bool isFunc_param=false, int numEvals=1000) const
	Computes the L2-distance between the field and a function func on the physical domain.
T	distanceL2 (gsFunctionSet< T > const &func, gsMultiBasis< T > const &B, bool isFunc_param=false, int numEvals=1000) const
const gsFunctionSet< T > &	fields () const
	Returns the fields (defined per patch)
const gsFunction< T > &	function (int i=0) const
	Returns the gsFunction of patch i.
short_t	geoDim () const
	Returns the dimension of the physical domain (e.g., if the domain is a surface in three-dimensional space, it returns 3).
const gsGeometry< T > &	igaFunction (int i=0) const
	Attempts to return an Isogeometric function for patch i.
bool	isParametric () const
bool	isParametrized () const
GISMO_DEPRECATED index_t	nPatches () const
	Returns the number of patches.
int	nPieces () const
	Returns the number of pieces.
short_t	parDim () const
	Returns the dimension of the parameter domain (e.g., if the domain is a surface in three-dimensional space, it returns 2).
const gsGeometry< T > &	patch (int i=0) const
	Returns the gsGeometry of patch i.
const gsMultiPatch< T > &	patches () const
	Returns gsMultiPatch containing the geometric information on the domain.
gsMatrix< T >	point (const gsMatrix< T > &u, int i=0) const
	Maps points u from the parameter domain to the physical domain. More...
std::ostream &	print (std::ostream &os) const
	Prints the object as a string.
gsMatrix< T >	value (const gsMatrix< T > &u, int i=0) const
	Evaluation of the field at points u. More...

Private Attributes
gsFunctionSet< T >::Ptr	m_fields
	Vector containing "local fields" for each patch/subdomain. More...
bool	m_parametric
	True iff this is an isogeometric field. More...
const gsFunctionSet< T > *	m_patches
	The isogeometric field is defined on this multipatch domain.

Member Function Documentation

const gsMatrix<T>& coefficientVector ( int  i = 0 ) const

inline

Returns the coefficient vector (if it exists) corresponding to the function field for patch i.

Returns the coefficients of the field corresponding to the i-th patch. This is only possible in the case when the field is defined in terms of basis functions (ie. it derives from gsGeometry).

T distanceDG	(	gsFunctionSet< T > const &	func,
		bool	isFunc_param = false,
		int	= 1000
	)		const

Computes the DG-distance between the field and a function func on the physical domain

T distanceH1	(	gsFunctionSet< T > const &	func,
		bool	isFunc_param = false,
		int	= 1000
	)		const

Computes the H1-seminorm of the diff. between the field and a function func on the physical domain

T distanceH1	(	gsFunctionSet< T > const &	func,
		gsMultiBasis< T > const &	B,
		bool	isFunc_param = false,
		int	= 1000
	)		const

Computes the H1-seminorm of the diff. between the field and a function func on the physical domain, using mesh from B

T distanceH2	(	gsFunctionSet< T > const &	func,
		bool	isFunc_param = false
	)		const

Computes the H2-seminorm of the diff. between the field and a function func on the physical domain, using mesh from B

T distanceL2	(	gsFunctionSet< T > const &	func,
		gsMultiBasis< T > const &	B,
		bool	isFunc_param = false,
		int	numEvals = 1000
	)		const

Computes the L2-distance between the field and a function func on the physical domain, using mesh from B

bool isParametric ( ) const

inline

True if the field function is defined on parametric coordinates (i.e. the same coordinate system as the patches)

bool isParametrized ( ) const

inline

True if the field function is parametrized by a set of basis functions in parametric coordinates (i.e. the same coordinate system as the patches)

gsMatrix<T> point ( const gsMatrix< T > &  u, int  i = 0  ) const

inline

Maps points u from the parameter domain to the physical domain.

Parameters

[in]	u	Evaluation points as gsMatrix of size d x n. d denotes the dimension of the parameter domain (i.e., d = parDim()). n denotes the number of evaluation points. Each column of u corresponds to one evaluation point.
[in]	i	Index of the considered patch/subdomain.

Returns

uPtr The j-th column of uPtr corresponds to the image of the point u_j (which is defined by the j-th column of the input parameter u).

gsMatrix<T> value ( const gsMatrix< T > &  u, int  i = 0  ) const

inline

Evaluation of the field at points u.

Parameters

[in]	u	Evaluation points as gsMatrix of size d x n. d denotes the dimension of the parameter domain (i.e., d = parDim()). n denotes the number of evaluation points. Each column of u corresponds to one evaluation point.
[in]	i	Index of the considered patch/subdomain.

Returns

uPtr The j-th column of uPtr corresponds to the value of the field at the point u_j (which is defined by the j-th column of the input parameter u).

Member Data Documentation

gsFunctionSet<T>::Ptr m_fields

private

Vector containing "local fields" for each patch/subdomain.

For each patch/subdomain, the "local field" is represented by a gsFunction. This local field can be accessed with gsField::function.

bool m_parametric

private

True iff this is an isogeometric field.

If m_parametric is true, the evaluation points for calling gsField::value have to be placed in the parameter domain.

If m_parametric is false, then the evaluation points are in the physical domain. This applies to, e.g., given exact solutions which are defined on the physical domain.