MFEM  v4.6.0 Finite element discretization library
fe_h1.hpp
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3 // LICENSE and NOTICE for details. LLNL-CODE-806117.
4 //
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7 //
8 // MFEM is free software; you can redistribute it and/or modify it under the
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10 // CONTRIBUTING.md for details.
11
12 #ifndef MFEM_FE_H1
13 #define MFEM_FE_H1
14
15 #include "fe_base.hpp"
16
17 namespace mfem
18 {
19
20 /// Arbitrary order H1 elements in 1D
22 {
23 private:
25  mutable Vector shape_x, dshape_x, d2shape_x;
26 #endif
27
28 public:
29  /// Construct the H1_SegmentElement of order @a p and BasisType @a btype
30  H1_SegmentElement(const int p, const int btype = BasisType::GaussLobatto);
31  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
32  virtual void CalcDShape(const IntegrationPoint &ip,
33  DenseMatrix &dshape) const;
34  virtual void CalcHessian(const IntegrationPoint &ip,
35  DenseMatrix &Hessian) const;
36  virtual void ProjectDelta(int vertex, Vector &dofs) const;
37 };
38
39
40 /// Arbitrary order H1 elements in 2D on a square
42 {
43 private:
45  mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
46 #endif
47
48 public:
49  /// Construct the H1_QuadrilateralElement of order @a p and BasisType @a btype
51  const int btype = BasisType::GaussLobatto);
52  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
53  virtual void CalcDShape(const IntegrationPoint &ip,
54  DenseMatrix &dshape) const;
55  virtual void CalcHessian(const IntegrationPoint &ip,
56  DenseMatrix &Hessian) const;
57  virtual void ProjectDelta(int vertex, Vector &dofs) const;
58 };
59
60
61 /// Arbitrary order H1 elements in 3D on a cube
63 {
64 private:
66  mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z,
67  d2shape_x, d2shape_y, d2shape_z;
68 #endif
69
70 public:
71  /// Construct the H1_HexahedronElement of order @a p and BasisType @a btype
72  H1_HexahedronElement(const int p, const int btype = BasisType::GaussLobatto);
73  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
74  virtual void CalcDShape(const IntegrationPoint &ip,
75  DenseMatrix &dshape) const;
76  virtual void CalcHessian(const IntegrationPoint &ip,
77  DenseMatrix &Hessian) const;
78  virtual void ProjectDelta(int vertex, Vector &dofs) const;
79 };
80
81
82 /// Arbitrary order H1 elements in 2D on a triangle
84 {
85 private:
87  mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
88  mutable Vector ddshape_x, ddshape_y, ddshape_l;
89  mutable DenseMatrix du, ddu;
90 #endif
92
93 public:
94  /// Construct the H1_TriangleElement of order @a p and BasisType @a btype
95  H1_TriangleElement(const int p, const int btype = BasisType::GaussLobatto);
96  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
97  virtual void CalcDShape(const IntegrationPoint &ip,
98  DenseMatrix &dshape) const;
99  virtual void CalcHessian(const IntegrationPoint &ip,
100  DenseMatrix &ddshape) const;
101 };
102
103
104 /// Arbitrary order H1 elements in 3D on a tetrahedron
106 {
107 private:
109  mutable Vector shape_x, shape_y, shape_z, shape_l;
110  mutable Vector dshape_x, dshape_y, dshape_z, dshape_l, u;
111  mutable Vector ddshape_x, ddshape_y, ddshape_z, ddshape_l;
112  mutable DenseMatrix du, ddu;
113 #endif
115
116 public:
117  /// Construct the H1_TetrahedronElement of order @a p and BasisType @a btype
118  H1_TetrahedronElement(const int p,
119  const int btype = BasisType::GaussLobatto);
120  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
121  virtual void CalcDShape(const IntegrationPoint &ip,
122  DenseMatrix &dshape) const;
123  virtual void CalcHessian(const IntegrationPoint &ip,
124  DenseMatrix &ddshape) const;
125 };
126
127
128
129 /// Arbitrary order H1 elements in 3D on a wedge
131 {
132 private:
134  mutable Vector t_shape, s_shape;
135  mutable DenseMatrix t_dshape, s_dshape;
136 #endif
137  Array<int> t_dof, s_dof;
138
139  H1_TriangleElement TriangleFE;
140  H1_SegmentElement SegmentFE;
141
142 public:
143  /// Construct the H1_WedgeElement of order @a p and BasisType @a btype
144  H1_WedgeElement(const int p,
145  const int btype = BasisType::GaussLobatto);
146  virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
147  virtual void CalcDShape(const IntegrationPoint &ip,
148  DenseMatrix &dshape) const;
149 };
150
151 } // namespace mfem
152
153 #endif
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 gi...
Definition: fe_h1.cpp:314
virtual void ProjectDelta(int vertex, Vector &dofs) const
Project a delta function centered on the given vertex in the local finite dimensional space represent...
Definition: fe_h1.cpp:216
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 gi...
Definition: fe_h1.cpp:783
Arbitrary order H1 elements in 2D on a square.
Definition: fe_h1.hpp:41
Data type dense matrix using column-major storage.
Definition: densemat.hpp:23
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 gi...
Definition: fe_h1.cpp:170
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 gi...
Definition: fe_h1.cpp:1018
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 giv...
Definition: fe_h1.cpp:78
H1_HexahedronElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_HexahedronElement of order p and BasisType btype.
Definition: fe_h1.cpp:265
virtual void ProjectDelta(int vertex, Vector &dofs) const
Project a delta function centered on the given vertex in the local finite dimensional space represent...
Definition: fe_h1.cpp:367
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...
Definition: fe_h1.cpp:40
Class for standard nodal finite elements.
Definition: fe_base.hpp:708
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &ddshape) const
Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the giv...
Definition: fe_h1.cpp:816
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...
Definition: fe_h1.cpp:758
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 gi...
Definition: fe_h1.cpp:555
H1_QuadrilateralElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_QuadrilateralElement of order p and BasisType btype.
Definition: fe_h1.cpp:125
Arbitrary order H1 elements in 3D on a tetrahedron.
Definition: fe_h1.hpp:105
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 gi...
Definition: fe_h1.cpp:59
H1_SegmentElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_SegmentElement of order p and BasisType btype.
Definition: fe_h1.cpp:21
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 giv...
Definition: fe_h1.cpp:192
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...
Definition: fe_h1.cpp:999
Arbitrary order H1 elements in 3D on a cube.
Definition: fe_h1.hpp:62
H1_TetrahedronElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_TetrahedronElement of order p and BasisType btype.
Definition: fe_h1.cpp:617
virtual void CalcHessian(const IntegrationPoint &ip, DenseMatrix &ddshape) const
Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the giv...
Definition: fe_h1.cpp:584
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...
Definition: fe_h1.cpp:533
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 giv...
Definition: fe_h1.cpp:338
H1_TriangleElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_TriangleElement of order p and BasisType btype.
Definition: fe_h1.cpp:451
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...
Definition: fe_h1.cpp:293
Class for integration point with weight.
Definition: intrules.hpp:31
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...
Definition: fe_h1.cpp:151
H1_WedgeElement(const int p, const int btype=BasisType::GaussLobatto)
Construct the H1_WedgeElement of order p and BasisType btype.
Definition: fe_h1.cpp:863
Arbitrary order H1 elements in 2D on a triangle.
Definition: fe_h1.hpp:83
Arbitrary order H1 elements in 1D.
Definition: fe_h1.hpp:21
Vector data type.
Definition: vector.hpp:58
virtual void ProjectDelta(int vertex, Vector &dofs) const
Project a delta function centered on the given vertex in the local finite dimensional space represent...
Definition: fe_h1.cpp:97
Arbitrary order H1 elements in 3D on a wedge.
Definition: fe_h1.hpp:130