gsL2Projection< T > Struct Template Reference

Detailed Description

template<class T>
struct gismo::gsL2Projection< T >

Class that performs an L2 projection.

Template Parameters

T	coefficient type

Static Public Member Functions
static T	project (const gsBasis< T > &projectionBasis, const gsBasis< T > &integrationBasis, const gsGeometry< T > &geometryMap, const gsFunction< T > &sourceFunction, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a function onto a basis.
static T	project (const gsBasis< T > &projectionBasis, const gsBasis< T > &integrationBasis, const gsGeometry< T > &geometryMap, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a geometry onto a basis (single patch)
static T	project (const gsBasis< T > &projectionBasis, const gsGeometry< T > &geometryMap, const gsFunction< T > &sourceFunction, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a function onto a basis.
static T	project (const gsBasis< T > &projectionBasis, const gsGeometry< T > &geometryMap, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a geometry onto a basis (single patch)
static T	project (const gsFunctionSet< T > &projectionBasis, const gsMultiBasis< T > &integrationBasis, const gsMultiPatch< T > &geometryMap, const gsFunctionSet< T > &sourceFunction, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a function onto a basis.
static T	project (const gsMultiBasis< T > &integrationBasis, const gsFunctionSet< T > &projectionBasis, const gsMultiPatch< T > &geometryMap, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a geometry onto a basis (multi-patch)
static T	project (const gsMultiBasis< T > &projectionBasis, const gsMultiPatch< T > &geometryMap, const gsFunctionSet< T > &sourceFunction, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a function onto a basis.
static T	project (const gsMultiBasis< T > &projectionBasis, const gsMultiPatch< T > &geometryMap, gsMatrix< T > &coefs, const gsOptionList &options=gsOptionList())
	Project a geometry onto a basis (multi-patch)
static GISMO_DEPRECATED T	projectFunction (const gsMultiBasis< T > &basis, const gsFunctionSet< T > &source, const gsMultiPatch< T > &geometry, gsMatrix< T > &result)
	Projects a function on a basis.
static GISMO_DEPRECATED T	projectFunction (const gsMultiBasis< T > &basis, const gsFunctionSet< T > &source, const gsMultiPatch< T > &geometry, gsMultiPatch< T > &result)
	Projects a function on a basis.
static GISMO_DEPRECATED T	projectFunction (const gsMultiBasis< T > &intbasis, const gsMappedBasis< 2, T > &basis, const gsFunctionSet< T > &source, const gsMultiPatch< T > &geometry, gsMatrix< T > &result)
	Projects a function on a basis.
static GISMO_DEPRECATED T	projectGeometry (const gsBasis< T > &basis, const gsGeometry< T > &geometry, gsMatrix< T > &result)
	Projects a source geometry onto basis and returns it in result.
static GISMO_DEPRECATED T	projectGeometry (const gsMultiBasis< T > &basis, const gsFunctionSet< T > &geometry, gsMatrix< T > &result)
	Projects a source geometry onto basis and returns it in result.
static GISMO_DEPRECATED T	projectGeometry (const gsMultiBasis< T > &basis, const gsFunctionSet< T > &geometry, gsMultiPatch< T > &result)
	Projects a source geometry onto basis and returns it in result.
static GISMO_DEPRECATED T	projectGeometry (const gsMultiBasis< T > &intbasis, const gsMappedBasis< 2, T > &basis, const gsFunctionSet< T > &geometry, gsMatrix< T > &result)
	Projects a source geometry onto basis and returns it in result.
static GISMO_DEPRECATED T	projectGeometryBoundaries (const gsMultiBasis< T > &basis, const gsMultiPatch< T > &geometry, gsMultiPatch< T > &result)
	Projects a source geometry onto basis and returns it in result. Fixes the boundaries.
static GISMO_DEPRECATED T	projectGeometryPenalty (const gsMultiBasis< T > &basis, const gsMultiPatch< T > &geometry, gsMultiPatch< T > &result, T penalty=1e3)
	Projects a source geometry onto basis and returns it in result. Penalizes interfaces and boundaries.

Static Protected Member Functions
static T	_project (const gsMultiBasis< T > &integrationBasis, const gsFunctionSet< T > &projectionBasis, const gsFunctionSet< T > &geometryMap, const gsFunctionSet< T > &sourceFunction, gsMatrix< T > &coefs, const gsOptionList &options)
	Projects a source function onto a projection basis using a geometry map.

Member Function Documentation

_project()

template<typename T >

T _project ( const gsMultiBasis< T > &  integrationBasis, const gsFunctionSet< T > &  projectionBasis, const gsFunctionSet< T > &  geometryMap, const gsFunctionSet< T > &  sourceFunction, gsMatrix< T > &  coefs, const gsOptionList &  options  )

staticprotected

Projects a source function onto a projection basis using a geometry map.

This function computes the coefficients of the projection of a given source function onto a projection basis. The projection is performed using a geometry map, which maps the integration domain to the physical domain.

Parameters

integrationBasis	The basis used for numerical integration.
projectionBasis	The basis functions used for the projection.
geometryMap	The geometry map that maps the integration domain to the physical domain.
sourceFunction	The source function to be projected.
coefs	The output matrix that stores the computed coefficients of the projection.
options	The options that control the projection process.

Returns

the projection error.

project() [1/8]

template<class T >

static T project ( const gsBasis< T > &  projectionBasis, const gsBasis< T > &  integrationBasis, const gsGeometry< T > &  geometryMap, const gsFunction< T > &  sourceFunction, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a function onto a basis.

Parameters

[in]	projectionBasis	The basis to project on
[in]	integrationBasis	The basis used for numerical integration.
[in]	geometryMap	The geometry
[in]	sourceFunction	The source function
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [2/8]

template<class T >

static T project ( const gsBasis< T > &  projectionBasis, const gsBasis< T > &  integrationBasis, const gsGeometry< T > &  geometryMap, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a geometry onto a basis (single patch)

Parameters

[in]	projectionBasis	The basis to project on
[in]	integrationBasis	The basis used for numerical integration.
[in]	geometryMap	The geometry
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [3/8]

template<class T >

static T project ( const gsBasis< T > &  projectionBasis, const gsGeometry< T > &  geometryMap, const gsFunction< T > &  sourceFunction, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a function onto a basis.

Parameters

[in]	projectionBasis	The basis to project on
[in]	geometryMap	The geometry
[in]	sourceFunction	The source function
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [4/8]

template<class T >

static T project ( const gsBasis< T > &  projectionBasis, const gsGeometry< T > &  geometryMap, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a geometry onto a basis (single patch)

Parameters

[in]	projectionBasis	The basis to project on
[in]	geometryMap	The geometry
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [5/8]

template<class T >

static T project ( const gsFunctionSet< T > &  projectionBasis, const gsMultiBasis< T > &  integrationBasis, const gsMultiPatch< T > &  geometryMap, const gsFunctionSet< T > &  sourceFunction, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a function onto a basis.

Parameters

[in]	projectionBasis	The basis to project on
[in]	integrationBasis	The basis used for numerical integration.
[in]	geometryMap	The geometry
[in]	sourceFunction	The source function
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [6/8]

template<class T >

static T project ( const gsMultiBasis< T > &  integrationBasis, const gsFunctionSet< T > &  projectionBasis, const gsMultiPatch< T > &  geometryMap, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a geometry onto a basis (multi-patch)

Parameters

[in]	projectionBasis	The basis to project on
[in]	integrationBasis	The basis used for numerical integration.
[in]	geometryMap	The geometry
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [7/8]

template<class T >

static T project ( const gsMultiBasis< T > &  projectionBasis, const gsMultiPatch< T > &  geometryMap, const gsFunctionSet< T > &  sourceFunction, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a function onto a basis.

Parameters

[in]	projectionBasis	The basis to project on
[in]	geometryMap	The geometry
[in]	sourceFunction	The source function
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

project() [8/8]

template<class T >

static T project ( const gsMultiBasis< T > &  projectionBasis, const gsMultiPatch< T > &  geometryMap, gsMatrix< T > &  coefs, const gsOptionList &  options = gsOptionList()  )

inlinestatic

Project a geometry onto a basis (multi-patch)

Parameters

[in]	projectionBasis	The basis to project on
[in]	geometryMap	The geometry
	coefs	The coefficients of the new geometry on projectionBasis

Returns

The L2 error of the projection

projectFunction() [1/3]

template<typename T >

T projectFunction ( const gsMultiBasis< T > &  basis, const gsFunctionSet< T > &  source, const gsMultiPatch< T > &  geometry, gsMatrix< T > &  result  )

static

Projects a function on a basis.

Parameters

[in]	basis	The basis to project on
[in]	source	The source function
[in]	geometry	The geometry to evaluate the function on
	result	The coefficients of the function

Returns

The L2 error of the projection

projectFunction() [2/3]

template<typename T >

T projectFunction ( const gsMultiBasis< T > &  basis, const gsFunctionSet< T > &  source, const gsMultiPatch< T > &  geometry, gsMultiPatch< T > &  result  )

static

Projects a function on a basis.

Parameters

[in]	basis	The basis to project on
[in]	source	The source function
[in]	geometry	The geometry to evaluate the function on
	result	The function as a multipatch

Returns

The L2 error of the projection

projectFunction() [3/3]

template<typename T >

T projectFunction ( const gsMultiBasis< T > &  intbasis, const gsMappedBasis< 2, T > &  basis, const gsFunctionSet< T > &  source, const gsMultiPatch< T > &  geometry, gsMatrix< T > &  result  )

static

Projects a function on a basis.

Parameters

[in]	intbasis	The basis used for quadrature
[in]	basis	The basis to project on
[in]	source	The source function
[in]	geometry	The geometry to evaluate the function on
	result	The function as a multipatch

Returns

The L2 error of the projection

projectGeometry() [1/4]

template<typename T >

T projectGeometry ( const gsBasis< T > &  basis, const gsGeometry< T > &  geometry, gsMatrix< T > &  result  )

static

Projects a source geometry onto basis and returns it in result.

Parameters

[in]	basis	The basis to project on
[in]	geometry	The geometry
	result	The coefficients of the new geometry on basis

Returns

The L2 error of the projection

projectGeometry() [2/4]

template<typename T >

T projectGeometry ( const gsMultiBasis< T > &  basis, const gsFunctionSet< T > &  geometry, gsMatrix< T > &  result  )

static

Projects a source geometry onto basis and returns it in result.

Parameters

[in]	basis	The basis to project on
[in]	geometry	The geometry
	result	The coefficients of the new geometry on basis

Returns

The L2 error of the projection

projectGeometry() [3/4]

template<typename T >

T projectGeometry ( const gsMultiBasis< T > &  basis, const gsFunctionSet< T > &  geometry, gsMultiPatch< T > &  result  )

static

Projects a source geometry onto basis and returns it in result.

Parameters

[in]	basis	The basis to project on
[in]	geometry	The geometry
	result	The new geometry

Returns

The L2 error of the projection

projectGeometry() [4/4]

template<typename T >

T projectGeometry ( const gsMultiBasis< T > &  intbasis, const gsMappedBasis< 2, T > &  basis, const gsFunctionSet< T > &  geometry, gsMatrix< T > &  result  )

static

Projects a source geometry onto basis and returns it in result.

Parameters

[in]	intbasis	The basis used for quadrature
[in]	basis	The mapped basis to project on
[in]	geometry	The geometry
	result	The coefficients of the new geometry on basis

Returns

The L2 error of the projection

projectGeometryBoundaries()

template<typename T >

T projectGeometryBoundaries ( const gsMultiBasis< T > &  basis, const gsMultiPatch< T > &  geometry, gsMultiPatch< T > &  result  )

static

Projects a source geometry onto basis and returns it in result. Fixes the boundaries.

Parameters

[in]	basis	The basis to project on
[in]	geometry	The geometry
	result	The coefficients of the new geometry on basis

Returns

The L2 error of the projection

projectGeometryPenalty()

template<typename T >

T projectGeometryPenalty ( const gsMultiBasis< T > &  basis, const gsMultiPatch< T > &  geometry, gsMultiPatch< T > &  result, T  penalty = 1e3  )

static

Projects a source geometry onto basis and returns it in result. Penalizes interfaces and boundaries.

Parameters

[in]	basis	The basis to project on
[in]	geometry	The geometry
	result	The coefficients of the new geometry on basis
[in]	penalty	The penalty factor

Returns

The L2 error of the projection