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// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
#ifndef MFEM_FE_COLLECTION
#define MFEM_FE_COLLECTION
#include "../config/config.hpp"
#include "geom.hpp"
#include "fe.hpp"
namespace mfem
{
/** @brief Collection of finite elements from the same family in multiple
dimensions. This class is used to match the degrees of freedom of a
FiniteElementSpace between elements, and to provide the finite element
restriction from an element to its boundary. */
class FiniteElementCollection
{
protected:
template <Geometry::Type geom>
static inline void GetNVE(int &nv, int &ne);
template <Geometry::Type geom, typename v_t>
static inline void GetEdge(int &nv, v_t &v, int &ne, int &e, int &eo,
const int edge_info);
template <Geometry::Type geom, Geometry::Type f_geom,
typename v_t, typename e_t, typename eo_t>
static inline void GetFace(int &nv, v_t &v, int &ne, e_t &e, eo_t &eo,
int &nf, int &f, Geometry::Type &fg, int &fo,
const int face_info);
public:
/** @brief Enumeration for ContType: defines the continuity of the field
across element interfaces. */
enum { CONTINUOUS, ///< Field is continuous across element interfaces
TANGENTIAL, ///< Tangential components of vector field
NORMAL, ///< Normal component of vector field
DISCONTINUOUS ///< Field is discontinuous across element interfaces
};
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const = 0;
virtual int DofForGeometry(Geometry::Type GeomType) const = 0;
/** @brief Returns an array, say p, that maps a local permuted index i to
a local base index: base_i = p[i]. */
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const = 0;
virtual const char * Name() const { return "Undefined"; }
virtual int GetContType() const = 0;
int HasFaceDofs(Geometry::Type GeomType) const;
virtual const FiniteElement *TraceFiniteElementForGeometry(
Geometry::Type GeomType) const
{
return FiniteElementForGeometry(GeomType);
}
virtual FiniteElementCollection *GetTraceCollection() const;
virtual ~FiniteElementCollection() { }
/** @brief Factory method: return a newly allocated FiniteElementCollection
according to the given name. */
/**
| FEC Name | Space | Order | BasisType | FiniteElement::MapT | Notes |
| :------: | :---: | :---: | :-------: | :-----: | :---: |
| H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
| H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
| H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
| H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
| H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
| H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
| ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
| ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
| ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
| ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
| RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
| RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
| RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
| RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
| RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
| RT_ValTrace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
| L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
| L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
| L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
| L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
| DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
| DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
| DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
| DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
| NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
| LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
| CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
| Local_[FENAME] | - | - | - | - | Special collection that builds a local version out of the FENAME collection |
|-|-|-|-|-|-|
| Linear | H1 | 1 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
| Quadratic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
| QuadraticPos | H1 | 2 | 2 | VALUE | Left in for backward compatibility, consider using H1_ |
| Cubic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
| Const2D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| Const3D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| LinearDiscont2D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| GaussLinearDiscont2D | L2 | 1 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
| P1OnQuad | H1 | 1 | 1 | VALUE | Linear P1 element with 3 nodes on a square |
| QuadraticDiscont2D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| QuadraticPosDiscont2D | L2 | 2 | 2 | VALUE | Left in for backward compatibility, consider using L2_ |
| GaussQuadraticDiscont2D | L2 | 2 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
| CubicDiscont2D | L2 | 3 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| LinearDiscont3D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| QuadraticDiscont3D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
| ND1_3D | H(Curl) | 1 | 1 / 0 | H_CURL | Left in for backward compatibility, consider using ND_ |
| RT0_2D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
| RT1_2D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
| RT2_2D | H(Div) | 3 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
| RT0_3D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
| RT1_3D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
| Tag | Description |
| :------: | :--------: |
| [DIM] | Dimension of the elements (1D, 2D, 3D) |
| [ORDER] | Approximation order of the elements (P0, P1, P2, ...) |
| [BTYPE] | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
| [OBTYPE] | Open BasisType of the element for elements which have both types |
| [CBTYPE] | Closed BasisType of the element for elements which have both types |
[FENAME] Is a special case for the Local FEC which generates a local version of a given
FEC. It is selected from one of (BiCubic2DFiniteElement, Quad_Q3, Nedelec1HexFiniteElement,
Hex_ND1, H1_[DIM]_[ORDER],H1Pos_[DIM]_[ORDER], L2_[DIM]_[ORDER] )
*/
static FiniteElementCollection *New(const char *name);
/** @brief Get the local dofs for a given sub-manifold.
Return the local dofs for a SDim-dimensional sub-manifold (0D - vertex, 1D
- edge, 2D - face) including those on its boundary. The local index of the
sub-manifold (inside Geom) and its orientation are given by the parameter
Info = 64 * SubIndex + SubOrientation. Naturally, it is assumed that 0 <=
SDim <= Dim(Geom). */
void SubDofOrder(Geometry::Type Geom, int SDim, int Info,
Array<int> &dofs) const;
};
/// Arbitrary order H1-conforming (continuous) finite elements.
class H1_FECollection : public FiniteElementCollection
{
protected:
int b_type;
char h1_name[32];
FiniteElement *H1_Elements[Geometry::NumGeom];
int H1_dof[Geometry::NumGeom];
int *SegDofOrd[2], *TriDofOrd[6], *QuadDofOrd[8], *TetDofOrd[24];
public:
explicit H1_FECollection(const int p, const int dim = 3,
const int btype = BasisType::GaussLobatto);
virtual const FiniteElement *FiniteElementForGeometry(
Geometry::Type GeomType) const
{ return H1_Elements[GeomType]; }
virtual int DofForGeometry(Geometry::Type GeomType) const
{ return H1_dof[GeomType]; }
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char *Name() const { return h1_name; }
virtual int GetContType() const { return CONTINUOUS; }
FiniteElementCollection *GetTraceCollection() const;
int GetBasisType() const { return b_type; }
/// Get the Cartesian to local H1 dof map
const int *GetDofMap(Geometry::Type GeomType) const;
virtual ~H1_FECollection();
};
/** @brief Arbitrary order H1-conforming (continuous) finite elements with
positive basis functions. */
class H1Pos_FECollection : public H1_FECollection
{
public:
explicit H1Pos_FECollection(const int p, const int dim = 3)
: H1_FECollection(p, dim, BasisType::Positive) { }
};
/** Arbitrary order H1-conforming (continuous) serendipity finite elements;
Current implementation works in 2D only; 3D version is in development. */
class H1Ser_FECollection : public H1_FECollection
{
public:
explicit H1Ser_FECollection(const int p, const int dim = 2)
: H1_FECollection(p, dim, BasisType::Serendipity) { };
};
/** @brief Arbitrary order "H^{1/2}-conforming" trace finite elements defined on
the interface between mesh elements (faces,edges,vertices); these are the
trace FEs of the H1-conforming FEs. */
class H1_Trace_FECollection : public H1_FECollection
{
public:
H1_Trace_FECollection(const int p, const int dim,
const int btype = BasisType::GaussLobatto);
};
/// Arbitrary order "L2-conforming" discontinuous finite elements.
class L2_FECollection : public FiniteElementCollection
{
private:
int b_type; // BasisType
char d_name[32];
ScalarFiniteElement *L2_Elements[Geometry::NumGeom];
ScalarFiniteElement *Tr_Elements[Geometry::NumGeom];
int *SegDofOrd[2]; // for rotating segment dofs in 1D
int *TriDofOrd[6]; // for rotating triangle dofs in 2D
int *TetDofOrd[24]; // for rotating tetrahedron dofs in 3D
int *OtherDofOrd; // for rotating other types of elements (for Or == 0)
public:
L2_FECollection(const int p, const int dim,
const int btype = BasisType::GaussLegendre,
const int map_type = FiniteElement::VALUE);
virtual const FiniteElement *FiniteElementForGeometry(
Geometry::Type GeomType) const
{
return L2_Elements[GeomType];
}
virtual int DofForGeometry(Geometry::Type GeomType) const
{
if (L2_Elements[GeomType])
{
return L2_Elements[GeomType]->GetDof();
}
return 0;
}
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char *Name() const { return d_name; }
virtual int GetContType() const { return DISCONTINUOUS; }
virtual const FiniteElement *TraceFiniteElementForGeometry(
Geometry::Type GeomType) const
{
return Tr_Elements[GeomType];
}
int GetBasisType() const { return b_type; }
virtual ~L2_FECollection();
};
/// Declare an alternative name for L2_FECollection = DG_FECollection
typedef L2_FECollection DG_FECollection;
/// Arbitrary order H(div)-conforming Raviart-Thomas finite elements.
class RT_FECollection : public FiniteElementCollection
{
protected:
int ob_type; // open BasisType
char rt_name[32];
FiniteElement *RT_Elements[Geometry::NumGeom];
int RT_dof[Geometry::NumGeom];
int *SegDofOrd[2], *TriDofOrd[6], *QuadDofOrd[8];
// Initialize only the face elements
void InitFaces(const int p, const int dim, const int map_type,
const bool signs);
// Constructor used by the constructor of the RT_Trace_FECollection and
// DG_Interface_FECollection classes
RT_FECollection(const int p, const int dim, const int map_type,
const bool signs,
const int ob_type = BasisType::GaussLegendre);
public:
RT_FECollection(const int p, const int dim,
const int cb_type = BasisType::GaussLobatto,
const int ob_type = BasisType::GaussLegendre);
virtual const FiniteElement *FiniteElementForGeometry(
Geometry::Type GeomType) const
{ return RT_Elements[GeomType]; }
virtual int DofForGeometry(Geometry::Type GeomType) const
{ return RT_dof[GeomType]; }
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char *Name() const { return rt_name; }
virtual int GetContType() const { return NORMAL; }
FiniteElementCollection *GetTraceCollection() const;
virtual ~RT_FECollection();
};
/** @brief Arbitrary order "H^{-1/2}-conforming" face finite elements defined on
the interface between mesh elements (faces); these are the normal trace FEs
of the H(div)-conforming FEs. */
class RT_Trace_FECollection : public RT_FECollection
{
public:
RT_Trace_FECollection(const int p, const int dim,
const int map_type = FiniteElement::INTEGRAL,
const int ob_type = BasisType::GaussLegendre);
};
/** Arbitrary order discontinuous finite elements defined on the interface
between mesh elements (faces). The functions in this space are single-valued
on each face and are discontinuous across its boundary. */
class DG_Interface_FECollection : public RT_FECollection
{
public:
DG_Interface_FECollection(const int p, const int dim,
const int map_type = FiniteElement::VALUE,
const int ob_type = BasisType::GaussLegendre);
};
/// Arbitrary order H(curl)-conforming Nedelec finite elements.
class ND_FECollection : public FiniteElementCollection
{
protected:
char nd_name[32];
FiniteElement *ND_Elements[Geometry::NumGeom];
int ND_dof[Geometry::NumGeom];
int *SegDofOrd[2], *TriDofOrd[6], *QuadDofOrd[8];
public:
ND_FECollection(const int p, const int dim,
const int cb_type = BasisType::GaussLobatto,
const int ob_type = BasisType::GaussLegendre);
virtual const FiniteElement *FiniteElementForGeometry(Geometry::Type GeomType)
const
{ return ND_Elements[GeomType]; }
virtual int DofForGeometry(Geometry::Type GeomType) const
{ return ND_dof[GeomType]; }
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char *Name() const { return nd_name; }
virtual int GetContType() const { return TANGENTIAL; }
FiniteElementCollection *GetTraceCollection() const;
virtual ~ND_FECollection();
};
/** @brief Arbitrary order H(curl)-trace finite elements defined on the
interface between mesh elements (faces,edges); these are the tangential
trace FEs of the H(curl)-conforming FEs. */
class ND_Trace_FECollection : public ND_FECollection
{
public:
ND_Trace_FECollection(const int p, const int dim,
const int cb_type = BasisType::GaussLobatto,
const int ob_type = BasisType::GaussLegendre);
};
/// Arbitrary order non-uniform rational B-splines (NURBS) finite elements.
class NURBSFECollection : public FiniteElementCollection
{
private:
NURBS1DFiniteElement *SegmentFE;
NURBS2DFiniteElement *QuadrilateralFE;
NURBS3DFiniteElement *ParallelepipedFE;
mutable int mOrder; // >= 1 or VariableOrder
// The 'name' can be:
// 1) name = "NURBS" + "number", for fixed order, or
// 2) name = "NURBS", for VariableOrder.
// The name is updated before writing it to a stream, for example, see
// FiniteElementSpace::Save().
mutable char name[16];
public:
enum { VariableOrder = -1 };
/** @brief The parameter @a Order must be either a positive number, for fixed
order, or VariableOrder (default). */
explicit NURBSFECollection(int Order = VariableOrder);
void Reset() const
{
SegmentFE->Reset();
QuadrilateralFE->Reset();
ParallelepipedFE->Reset();
}
/** @brief Get the order of the NURBS collection: either a positive number,
when using fixed order, or VariableOrder. */
int GetOrder() const { return mOrder; }
/** @brief Set the order and the name, based on the given @a Order: either a
positive number for fixed order, or VariableOrder. */
void SetOrder(int Order) const;
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char *Name() const { return name; }
virtual int GetContType() const { return CONTINUOUS; }
FiniteElementCollection *GetTraceCollection() const;
virtual ~NURBSFECollection();
};
/// Piecewise-(bi/tri)linear continuous finite elements.
class LinearFECollection : public FiniteElementCollection
{
private:
const PointFiniteElement PointFE;
const Linear1DFiniteElement SegmentFE;
const Linear2DFiniteElement TriangleFE;
const BiLinear2DFiniteElement QuadrilateralFE;
const Linear3DFiniteElement TetrahedronFE;
const TriLinear3DFiniteElement ParallelepipedFE;
const H1_WedgeElement WedgeFE;
public:
LinearFECollection() : WedgeFE(1) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "Linear"; }
virtual int GetContType() const { return CONTINUOUS; }
};
/// Piecewise-(bi)quadratic continuous finite elements.
class QuadraticFECollection : public FiniteElementCollection
{
private:
const PointFiniteElement PointFE;
const Quad1DFiniteElement SegmentFE;
const Quad2DFiniteElement TriangleFE;
const BiQuad2DFiniteElement QuadrilateralFE;
const Quadratic3DFiniteElement TetrahedronFE;
const LagrangeHexFiniteElement ParallelepipedFE;
const H1_WedgeElement WedgeFE;
public:
QuadraticFECollection() : ParallelepipedFE(2), WedgeFE(2) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "Quadratic"; }
virtual int GetContType() const { return CONTINUOUS; }
};
/// Version of QuadraticFECollection with positive basis functions.
class QuadraticPosFECollection : public FiniteElementCollection
{
private:
const QuadPos1DFiniteElement SegmentFE;
const BiQuadPos2DFiniteElement QuadrilateralFE;
public:
QuadraticPosFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "QuadraticPos"; }
virtual int GetContType() const { return CONTINUOUS; }
};
/// Piecewise-(bi)cubic continuous finite elements.
class CubicFECollection : public FiniteElementCollection
{
private:
const PointFiniteElement PointFE;
const Cubic1DFiniteElement SegmentFE;
const Cubic2DFiniteElement TriangleFE;
const BiCubic2DFiniteElement QuadrilateralFE;
const Cubic3DFiniteElement TetrahedronFE;
const LagrangeHexFiniteElement ParallelepipedFE;
const H1_WedgeElement WedgeFE;
public:
CubicFECollection()
: ParallelepipedFE(3), WedgeFE(3, BasisType::ClosedUniform) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "Cubic"; }
virtual int GetContType() const { return CONTINUOUS; }
};
/// Crouzeix-Raviart nonconforming elements in 2D.
class CrouzeixRaviartFECollection : public FiniteElementCollection
{
private:
const P0SegmentFiniteElement SegmentFE;
const CrouzeixRaviartFiniteElement TriangleFE;
const CrouzeixRaviartQuadFiniteElement QuadrilateralFE;
public:
CrouzeixRaviartFECollection() : SegmentFE(1) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "CrouzeixRaviart"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Piecewise-linear nonconforming finite elements in 3D.
class LinearNonConf3DFECollection : public FiniteElementCollection
{
private:
const P0TriangleFiniteElement TriangleFE;
const P1TetNonConfFiniteElement TetrahedronFE;
const P0QuadFiniteElement QuadrilateralFE;
const RotTriLinearHexFiniteElement ParallelepipedFE;
public:
LinearNonConf3DFECollection () { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "LinearNonConf3D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief First order Raviart-Thomas finite elements in 2D. This class is kept
only for backward compatibility, consider using RT_FECollection instead. */
class RT0_2DFECollection : public FiniteElementCollection
{
private:
const P0SegmentFiniteElement SegmentFE; // normal component on edge
const RT0TriangleFiniteElement TriangleFE;
const RT0QuadFiniteElement QuadrilateralFE;
public:
RT0_2DFECollection() : SegmentFE(0) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RT0_2D"; }
virtual int GetContType() const { return NORMAL; }
};
/** @brief Second order Raviart-Thomas finite elements in 2D. This class is kept
only for backward compatibility, consider using RT_FECollection instead. */
class RT1_2DFECollection : public FiniteElementCollection
{
private:
const P1SegmentFiniteElement SegmentFE; // normal component on edge
const RT1TriangleFiniteElement TriangleFE;
const RT1QuadFiniteElement QuadrilateralFE;
public:
RT1_2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RT1_2D"; }
virtual int GetContType() const { return NORMAL; }
};
/** @brief Third order Raviart-Thomas finite elements in 2D. This class is kept
only for backward compatibility, consider using RT_FECollection instead. */
class RT2_2DFECollection : public FiniteElementCollection
{
private:
const P2SegmentFiniteElement SegmentFE; // normal component on edge
const RT2TriangleFiniteElement TriangleFE;
const RT2QuadFiniteElement QuadrilateralFE;
public:
RT2_2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RT2_2D"; }
virtual int GetContType() const { return NORMAL; }
};
/** @brief Piecewise-constant discontinuous finite elements in 2D. This class is
kept only for backward compatibility, consider using L2_FECollection
instead. */
class Const2DFECollection : public FiniteElementCollection
{
private:
const P0TriangleFiniteElement TriangleFE;
const P0QuadFiniteElement QuadrilateralFE;
public:
Const2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "Const2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-linear discontinuous finite elements in 2D. This class is
kept only for backward compatibility, consider using L2_FECollection
instead. */
class LinearDiscont2DFECollection : public FiniteElementCollection
{
private:
const Linear2DFiniteElement TriangleFE;
const BiLinear2DFiniteElement QuadrilateralFE;
public:
LinearDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "LinearDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Version of LinearDiscont2DFECollection with dofs in the Gaussian points.
class GaussLinearDiscont2DFECollection : public FiniteElementCollection
{
private:
// const CrouzeixRaviartFiniteElement TriangleFE;
const GaussLinear2DFiniteElement TriangleFE;
const GaussBiLinear2DFiniteElement QuadrilateralFE;
public:
GaussLinearDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "GaussLinearDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Linear (P1) finite elements on quadrilaterals.
class P1OnQuadFECollection : public FiniteElementCollection
{
private:
const P1OnQuadFiniteElement QuadrilateralFE;
public:
P1OnQuadFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "P1OnQuad"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-quadratic discontinuous finite elements in 2D. This class
is kept only for backward compatibility, consider using L2_FECollection
instead. */
class QuadraticDiscont2DFECollection : public FiniteElementCollection
{
private:
const Quad2DFiniteElement TriangleFE;
const BiQuad2DFiniteElement QuadrilateralFE;
public:
QuadraticDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "QuadraticDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Version of QuadraticDiscont2DFECollection with positive basis functions.
class QuadraticPosDiscont2DFECollection : public FiniteElementCollection
{
private:
const BiQuadPos2DFiniteElement QuadrilateralFE;
public:
QuadraticPosDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const
{ return NULL; }
virtual const char * Name() const { return "QuadraticPosDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Version of QuadraticDiscont2DFECollection with dofs in the Gaussian points.
class GaussQuadraticDiscont2DFECollection : public FiniteElementCollection
{
private:
// const Quad2DFiniteElement TriangleFE;
const GaussQuad2DFiniteElement TriangleFE;
const GaussBiQuad2DFiniteElement QuadrilateralFE;
public:
GaussQuadraticDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "GaussQuadraticDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-cubic discontinuous finite elements in 2D. This class is
kept only for backward compatibility, consider using L2_FECollection
instead. */
class CubicDiscont2DFECollection : public FiniteElementCollection
{
private:
const Cubic2DFiniteElement TriangleFE;
const BiCubic2DFiniteElement QuadrilateralFE;
public:
CubicDiscont2DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "CubicDiscont2D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-constant discontinuous finite elements in 3D. This class is
kept only for backward compatibility, consider using L2_FECollection
instead. */
class Const3DFECollection : public FiniteElementCollection
{
private:
const P0TetFiniteElement TetrahedronFE;
const P0HexFiniteElement ParallelepipedFE;
const L2_WedgeElement WedgeFE;
public:
Const3DFECollection() : WedgeFE(0) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "Const3D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-linear discontinuous finite elements in 3D. This class is
kept only for backward compatibility, consider using L2_FECollection
instead. */
class LinearDiscont3DFECollection : public FiniteElementCollection
{
private:
const Linear3DFiniteElement TetrahedronFE;
const TriLinear3DFiniteElement ParallelepipedFE;
public:
LinearDiscont3DFECollection () { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "LinearDiscont3D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/** @brief Piecewise-quadratic discontinuous finite elements in 3D. This class
is kept only for backward compatibility, consider using L2_FECollection
instead. */
class QuadraticDiscont3DFECollection : public FiniteElementCollection
{
private:
const Quadratic3DFiniteElement TetrahedronFE;
const LagrangeHexFiniteElement ParallelepipedFE;
public:
QuadraticDiscont3DFECollection () : ParallelepipedFE(2) { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "QuadraticDiscont3D"; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
/// Finite element collection on a macro-element.
class RefinedLinearFECollection : public FiniteElementCollection
{
private:
const PointFiniteElement PointFE;
const RefinedLinear1DFiniteElement SegmentFE;
const RefinedLinear2DFiniteElement TriangleFE;
const RefinedBiLinear2DFiniteElement QuadrilateralFE;
const RefinedLinear3DFiniteElement TetrahedronFE;
const RefinedTriLinear3DFiniteElement ParallelepipedFE;
public:
RefinedLinearFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RefinedLinear"; }
virtual int GetContType() const { return CONTINUOUS; }
};
/** @brief Lowest order Nedelec finite elements in 3D. This class is kept only
for backward compatibility, consider using the new ND_FECollection
instead. */
class ND1_3DFECollection : public FiniteElementCollection
{
private:
const Nedelec1HexFiniteElement HexahedronFE;
const Nedelec1TetFiniteElement TetrahedronFE;
public:
ND1_3DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "ND1_3D"; }
virtual int GetContType() const { return TANGENTIAL; }
};
/** @brief First order Raviart-Thomas finite elements in 3D. This class is kept
only for backward compatibility, consider using RT_FECollection instead. */
class RT0_3DFECollection : public FiniteElementCollection
{
private:
const P0TriangleFiniteElement TriangleFE;
const P0QuadFiniteElement QuadrilateralFE;
const RT0HexFiniteElement HexahedronFE;
const RT0TetFiniteElement TetrahedronFE;
public:
RT0_3DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RT0_3D"; }
virtual int GetContType() const { return NORMAL; }
};
/** @brief Second order Raviart-Thomas finite elements in 3D. This class is kept
only for backward compatibility, consider using RT_FECollection instead. */
class RT1_3DFECollection : public FiniteElementCollection
{
private:
const Linear2DFiniteElement TriangleFE;
const BiLinear2DFiniteElement QuadrilateralFE;
const RT1HexFiniteElement HexahedronFE;
public:
RT1_3DFECollection() { }
virtual const FiniteElement *
FiniteElementForGeometry(Geometry::Type GeomType) const;
virtual int DofForGeometry(Geometry::Type GeomType) const;
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const;
virtual const char * Name() const { return "RT1_3D"; }
virtual int GetContType() const { return NORMAL; }
};
/// Discontinuous collection defined locally by a given finite element.
class Local_FECollection : public FiniteElementCollection
{
private:
char d_name[32];
Geometry::Type GeomType;
FiniteElement *Local_Element;
public:
Local_FECollection(const char *fe_name);
virtual const FiniteElement *FiniteElementForGeometry(
Geometry::Type _GeomType) const
{ return (GeomType == _GeomType) ? Local_Element : NULL; }
virtual int DofForGeometry(Geometry::Type _GeomType) const
{ return (GeomType == _GeomType) ? Local_Element->GetDof() : 0; }
virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
int Or) const
{ return NULL; }
virtual const char *Name() const { return d_name; }
virtual ~Local_FECollection() { delete Local_Element; }
virtual int GetContType() const { return DISCONTINUOUS; }
};
}
#endif
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