MFEM v4.7.0
Finite element discretization library
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Public Member Functions | Protected Attributes | List of all members
mfem::NURBS1DFiniteElement Class Reference

An arbitrary order 1D NURBS element on a segment. More...

#include <fe_nurbs.hpp>

Inheritance diagram for mfem::NURBS1DFiniteElement:
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Collaboration diagram for mfem::NURBS1DFiniteElement:
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Public Member Functions

 NURBS1DFiniteElement (int p)
 Construct the NURBS1DFiniteElement of order p.
 
virtual void SetOrder () const
 Update the NURBSFiniteElement according to the currently set knot vectors.
 
virtual void CalcShape (const IntegrationPoint &ip, Vector &shape) const
 Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.
 
virtual void CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const
 Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.
 
virtual void CalcHessian (const IntegrationPoint &ip, DenseMatrix &hessian) const
 Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.
 
- Public Member Functions inherited from mfem::NURBSFiniteElement
 NURBSFiniteElement (int D, Geometry::Type G, int Do, int O, int F)
 Construct NURBSFiniteElement with given.
 
void Reset () const
 
void SetIJK (const int *IJK) const
 
int GetPatch () const
 
void SetPatch (int p) const
 
int GetElement () const
 
void SetElement (int e) const
 
Array< const KnotVector * > & KnotVectors () const
 
VectorWeights () const
 
virtual void SetOrder () const
 Update the NURBSFiniteElement according to the currently set knot vectors.
 
const int * GetIJK () const
 
- Public Member Functions inherited from mfem::ScalarFiniteElement
 ScalarFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
 Construct ScalarFiniteElement with given.
 
virtual void SetMapType (int M)
 Set the FiniteElement::MapType of the element to either VALUE or INTEGRAL. Also sets the FiniteElement::DerivType to GRAD if the FiniteElement::MapType is VALUE.
 
void NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
 Get the matrix I that defines nodal interpolation between this element and the refined element fine_fe.
 
void ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
 Get matrix I "Interpolation" defined through local L2-projection in the space defined by the fine_fe.
 
void ScalarLocalL2Restriction (ElementTransformation &Trans, DenseMatrix &R, const ScalarFiniteElement &coarse_fe) const
 Get restriction matrix R defined through local L2-projection in the space defined by the coarse_fe.
 
- Public Member Functions inherited from mfem::FiniteElement
 FiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
 Construct FiniteElement with given.
 
int GetDim () const
 Returns the reference space dimension for the finite element.
 
int GetRangeDim () const
 Returns the vector dimension for vector-valued finite elements, which is also the dimension of the interpolation operation.
 
int GetCurlDim () const
 Returns the dimension of the curl for vector-valued finite elements.
 
Geometry::Type GetGeomType () const
 Returns the Geometry::Type of the reference element.
 
int GetDof () const
 Returns the number of degrees of freedom in the finite element.
 
int GetOrder () const
 Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.
 
bool HasAnisotropicOrders () const
 Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.
 
const int * GetAnisotropicOrders () const
 Returns an array containing the anisotropic orders/degrees.
 
int Space () const
 Returns the type of FunctionSpace on the element.
 
int GetRangeType () const
 Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}.
 
int GetDerivRangeType () const
 Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR.
 
int GetMapType () const
 Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}.
 
int GetDerivType () const
 Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}.
 
int GetDerivMapType () const
 Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}.
 
virtual void CalcShape (const IntegrationPoint &ip, Vector &shape) const =0
 Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.
 
void CalcPhysShape (ElementTransformation &Trans, Vector &shape) const
 Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans.
 
virtual void CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0
 Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.
 
void CalcPhysDShape (ElementTransformation &Trans, DenseMatrix &dshape) const
 Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans.
 
const IntegrationRuleGetNodes () const
 Get a const reference to the nodes of the element.
 
virtual void CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const
 Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip.
 
virtual void CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const
 Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.
 
void CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
 Equivalent to the CalcVShape() method with the same arguments.
 
virtual void CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const
 Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip.
 
void CalcPhysDivShape (ElementTransformation &Trans, Vector &divshape) const
 Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans.
 
virtual void CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const
 Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip.
 
virtual void CalcPhysCurlShape (ElementTransformation &Trans, DenseMatrix &curl_shape) const
 Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans.
 
virtual void GetFaceDofs (int face, int **dofs, int *ndofs) const
 Get the dofs associated with the given face. *dofs is set to an internal array of the local dofc on the face, while *ndofs is set to the number of dofs on that face.
 
virtual void CalcHessian (const IntegrationPoint &ip, DenseMatrix &Hessian) const
 Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.
 
virtual void CalcPhysHessian (ElementTransformation &Trans, DenseMatrix &Hessian) const
 Evaluate the Hessian of all shape functions of a scalar finite element in reference space at the given point ip.
 
virtual void CalcPhysLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
 Evaluate the Laplacian of all shape functions of a scalar finite element in reference space at the given point ip.
 
virtual void CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
 
virtual void GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const
 Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.
 
virtual void GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
 Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.
 
virtual void GetTransferMatrix (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element.
 
virtual void Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom.
 
virtual void Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 Given a vector coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. (VectorFiniteElements)
 
virtual void ProjectFromNodes (Vector &vc, ElementTransformation &Trans, Vector &dofs) const
 Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements.
 
virtual void ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
 Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space.
 
virtual void ProjectDelta (int vertex, Vector &dofs) const
 Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs.
 
virtual void Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.
 
virtual void ProjectGrad (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
 Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
 
virtual void ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
 Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
 
virtual void ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
 Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.
 
virtual const DofToQuadGetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const
 Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode.
 
virtual void GetFaceMap (const int face_id, Array< int > &face_map) const
 Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id.
 
virtual const StatelessDofTransformationGetDofTransformation () const
 Return a DoF transformation object for this particular type of basis.
 
virtual ~FiniteElement ()
 Deconstruct the FiniteElement.
 

Protected Attributes

Vector shape_x
 
- Protected Attributes inherited from mfem::NURBSFiniteElement
Array< const KnotVector * > kv
 
const int * ijk
 
int patch
 
int elem
 
Vector weights
 
- Protected Attributes inherited from mfem::FiniteElement
int dim
 Dimension of reference space.
 
int vdim
 Vector dimension of vector-valued basis functions.
 
int cdim
 Dimension of curl for vector-valued basis functions.
 
Geometry::Type geom_type
 Geometry::Type of the reference element.
 
int func_space
 
int range_type
 
int map_type
 
int deriv_type
 
int deriv_range_type
 
int deriv_map_type
 
int dof
 Number of degrees of freedom.
 
int order
 Order/degree of the shape functions.
 
int orders [Geometry::MaxDim]
 Anisotropic orders.
 
IntegrationRule Nodes
 
DenseMatrix vshape
 
Array< DofToQuad * > dof2quad_array
 Container for all DofToQuad objects created by the FiniteElement.
 

Additional Inherited Members

- Public Types inherited from mfem::FiniteElement
enum  RangeType { UNKNOWN_RANGE_TYPE = -1 , SCALAR , VECTOR }
 Enumeration for range_type and deriv_range_type. More...
 
enum  MapType {
  UNKNOWN_MAP_TYPE = -1 , VALUE , INTEGRAL , H_DIV ,
  H_CURL
}
 Enumeration for MapType: defines how reference functions are mapped to physical space. More...
 
enum  DerivType { NONE , GRAD , DIV , CURL }
 Enumeration for DerivType: defines which derivative method is implemented. More...
 
- Static Public Member Functions inherited from mfem::FiniteElement
static bool IsClosedType (int b_type)
 Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary).
 
static bool IsOpenType (int b_type)
 Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).
 
static int VerifyClosed (int b_type)
 Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary).
 
static int VerifyOpen (int b_type)
 Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).
 
static int VerifyNodal (int b_type)
 Ensure that the BasisType of b_type nodal (satisfies the interpolation property).
 
- Static Protected Member Functions inherited from mfem::ScalarFiniteElement
static const ScalarFiniteElementCheckScalarFE (const FiniteElement &fe)
 

Detailed Description

An arbitrary order 1D NURBS element on a segment.

Definition at line 67 of file fe_nurbs.hpp.

Constructor & Destructor Documentation

◆ NURBS1DFiniteElement()

mfem::NURBS1DFiniteElement::NURBS1DFiniteElement ( int  p)
inline

Construct the NURBS1DFiniteElement of order p.

Definition at line 74 of file fe_nurbs.hpp.

Member Function Documentation

◆ CalcDShape()

void mfem::NURBS1DFiniteElement::CalcDShape ( const IntegrationPoint ip,
DenseMatrix dshape 
) const
virtual

Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (dof x dim) of dshape must be set in advance.

Implements mfem::FiniteElement.

Definition at line 45 of file fe_nurbs.cpp.

◆ CalcHessian()

void mfem::NURBS1DFiniteElement::CalcHessian ( const IntegrationPoint ip,
DenseMatrix Hessian 
) const
virtual

Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix Hessian contains upper triangular part of the Hessian of one shape function. The order in 2D is {u_xx, u_xy, u_yy}. The size (dof x (dim (dim+1)/2) of Hessian must be set in advance.

Reimplemented from mfem::FiniteElement.

Definition at line 64 of file fe_nurbs.cpp.

◆ CalcShape()

void mfem::NURBS1DFiniteElement::CalcShape ( const IntegrationPoint ip,
Vector shape 
) const
virtual

Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.

The size (dof) of the result Vector shape must be set in advance.

Implements mfem::FiniteElement.

Definition at line 31 of file fe_nurbs.cpp.

◆ SetOrder()

void mfem::NURBS1DFiniteElement::SetOrder ( ) const
virtual

Update the NURBSFiniteElement according to the currently set knot vectors.

Reimplemented from mfem::NURBSFiniteElement.

Definition at line 22 of file fe_nurbs.cpp.

Member Data Documentation

◆ shape_x

Vector mfem::NURBS1DFiniteElement::shape_x
mutableprotected

Definition at line 70 of file fe_nurbs.hpp.


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