libMesh
Public Member Functions | Private Attributes | List of all members
DivGradExactSolution Class Reference

#include <div_grad_exact_solution.h>

Public Member Functions

 DivGradExactSolution ()=default
 
 ~DivGradExactSolution ()=default
 
Real scalar (Real x, Real y)
 
Real scalar (Real x, Real y, Real z)
 
RealGradient operator() (Real x, Real y)
 
RealGradient operator() (Real x, Real y, Real z)
 
RealTensor grad (Real x, Real y)
 
RealTensor grad (Real x, Real y, Real z)
 
Real div (Real x, Real y)
 
Real div (Real x, Real y, Real z)
 
Real forcing (Real x, Real y)
 
Real forcing (Real x, Real y, Real z)
 
 DivGradExactSolution ()=default
 
 ~DivGradExactSolution ()=default
 
Real scalar (Real x, Real y)
 
Real scalar (Real x, Real y, Real z)
 
RealGradient operator() (Real x, Real y)
 
RealGradient operator() (Real x, Real y, Real z)
 
RealTensor grad (Real x, Real y)
 
RealTensor grad (Real x, Real y, Real z)
 
Real div (Real x, Real y)
 
Real div (Real x, Real y, Real z)
 
Real forcing (Real x, Real y)
 
Real forcing (Real x, Real y, Real z)
 

Private Attributes

const Real k = .5*pi
 

Detailed Description

Definition at line 26 of file div_grad_exact_solution.h.

Constructor & Destructor Documentation

◆ DivGradExactSolution() [1/2]

DivGradExactSolution::DivGradExactSolution ( )
default

◆ ~DivGradExactSolution() [1/2]

DivGradExactSolution::~DivGradExactSolution ( )
default

◆ DivGradExactSolution() [2/2]

DivGradExactSolution::DivGradExactSolution ( )
default

◆ ~DivGradExactSolution() [2/2]

DivGradExactSolution::~DivGradExactSolution ( )
default

Member Function Documentation

◆ div() [1/4]

Real DivGradExactSolution::div ( Real  x,
Real  y 
)
inline

Definition at line 84 of file div_grad_exact_solution.h.

References libMesh::Real.

85  {
86  const Real dux_dx = grad(x, y)(0, 0);
87  const Real duy_dy = grad(x, y)(1, 1);
88 
89  return dux_dx + duy_dy;
90  }
DivGradExactSolution::grad
RealTensor grad(Real x, Real y)
Definition: div_grad_exact_solution.h:59
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ div() [2/4]

Real DivGradExactSolution::div ( Real  x,
Real  y 
)
inline

Definition at line 84 of file div_grad_exact_solution.h.

References libMesh::Real.

85  {
86  const Real dux_dx = grad(x, y)(0, 0);
87  const Real duy_dy = grad(x, y)(1, 1);
88 
89  return dux_dx + duy_dy;
90  }
DivGradExactSolution::grad
RealTensor grad(Real x, Real y)
Definition: div_grad_exact_solution.h:59
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ div() [3/4]

Real DivGradExactSolution::div ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 92 of file div_grad_exact_solution.h.

References libMesh::Real.

93  {
94  const Real dux_dx = grad(x, y, z)(0, 0);
95  const Real duy_dy = grad(x, y, z)(1, 1);
96  const Real duz_dz = grad(x, y, z)(2, 2);
97 
98  return dux_dx + duy_dy + duz_dz;
99  }
DivGradExactSolution::grad
RealTensor grad(Real x, Real y)
Definition: div_grad_exact_solution.h:59
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ div() [4/4]

Real DivGradExactSolution::div ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 92 of file div_grad_exact_solution.h.

References libMesh::Real.

93  {
94  const Real dux_dx = grad(x, y, z)(0, 0);
95  const Real duy_dy = grad(x, y, z)(1, 1);
96  const Real duz_dz = grad(x, y, z)(2, 2);
97 
98  return dux_dx + duy_dy + duz_dz;
99  }
DivGradExactSolution::grad
RealTensor grad(Real x, Real y)
Definition: div_grad_exact_solution.h:59
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ forcing() [1/4]

Real DivGradExactSolution::forcing ( Real  x,
Real  y 
)
inline

Definition at line 101 of file div_grad_exact_solution.h.

Referenced by assemble_divgrad(), and fe_assembly().

102  {
103  return div(x, y);
104  }
DivGradExactSolution::div
Real div(Real x, Real y)
Definition: div_grad_exact_solution.h:84

◆ forcing() [2/4]

Real DivGradExactSolution::forcing ( Real  x,
Real  y 
)
inline

Definition at line 101 of file div_grad_exact_solution.h.

102  {
103  return div(x, y);
104  }
DivGradExactSolution::div
Real div(Real x, Real y)
Definition: div_grad_exact_solution.h:84

◆ forcing() [3/4]

Real DivGradExactSolution::forcing ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 106 of file div_grad_exact_solution.h.

107  {
108  return div(x, y, z);
109  }
DivGradExactSolution::div
Real div(Real x, Real y)
Definition: div_grad_exact_solution.h:84

◆ forcing() [4/4]

Real DivGradExactSolution::forcing ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 106 of file div_grad_exact_solution.h.

107  {
108  return div(x, y, z);
109  }
DivGradExactSolution::div
Real div(Real x, Real y)
Definition: div_grad_exact_solution.h:84

◆ grad() [1/4]

RealTensor DivGradExactSolution::grad ( Real  x,
Real  y 
)
inline

Definition at line 59 of file div_grad_exact_solution.h.

References libMesh::Real.

60  {
61  const Real dux_dx = k*k*cos(k*x)*sin(k*y);
62  const Real dux_dy = k*k*sin(k*x)*cos(k*y);
63  const Real duy_dx = k*k*sin(k*x)*cos(k*y);
64  const Real duy_dy = k*k*cos(k*x)*sin(k*y);
65 
66  return RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy);
67  }
libMesh::RealTensor
RealTensorValue RealTensor
Definition: hp_coarsentest.h:50
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ grad() [2/4]

RealTensor DivGradExactSolution::grad ( Real  x,
Real  y 
)
inline

Definition at line 59 of file div_grad_exact_solution.h.

References libMesh::pi, and libMesh::Real.

60  {
61  const Real dux_dx = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
62  const Real dux_dy = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
63  const Real duy_dx = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
64  const Real duy_dy = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
65 
66  return RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy);
67  }
libMesh::RealTensor
RealTensorValue RealTensor
Definition: hp_coarsentest.h:50
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

◆ grad() [3/4]

RealTensor DivGradExactSolution::grad ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 69 of file div_grad_exact_solution.h.

References libMesh::pi, and libMesh::Real.

70  {
71  const Real dux_dx = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
72  const Real dux_dy = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
73  const Real dux_dz = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
74  const Real duy_dx = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
75  const Real duy_dy = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
76  const Real duy_dz = .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
77  const Real duz_dx = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
78  const Real duz_dy = .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
79  const Real duz_dz = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
80 
81  return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
82  }
libMesh::RealTensor
RealTensorValue RealTensor
Definition: hp_coarsentest.h:50
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

◆ grad() [4/4]

RealTensor DivGradExactSolution::grad ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 69 of file div_grad_exact_solution.h.

References libMesh::Real.

70  {
71  const Real dux_dx = k*k*cos(k*x)*sin(k*y)*cos(k*z);
72  const Real dux_dy = k*k*sin(k*x)*cos(k*y)*cos(k*z);
73  const Real dux_dz = -k*k*sin(k*x)*sin(k*y)*sin(k*z);
74  const Real duy_dx = k*k*sin(k*x)*cos(k*y)*cos(k*z);
75  const Real duy_dy = k*k*cos(k*x)*sin(k*y)*cos(k*z);
76  const Real duy_dz = k*k*cos(k*x)*cos(k*y)*sin(k*z);
77  const Real duz_dx = -k*k*sin(k*x)*sin(k*y)*sin(k*z);
78  const Real duz_dy = k*k*cos(k*x)*cos(k*y)*sin(k*z);
79  const Real duz_dz = k*k*cos(k*x)*sin(k*y)*cos(k*z);
80 
81  return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
82  }
libMesh::RealTensor
RealTensorValue RealTensor
Definition: hp_coarsentest.h:50
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ operator()() [1/4]

RealGradient DivGradExactSolution::operator() ( Real  x,
Real  y 
)
inline

Definition at line 42 of file div_grad_exact_solution.h.

References libMesh::Real.

43  {
44  const Real ux = k*sin(k*x)*sin(k*y);
45  const Real uy = -k*cos(k*x)*cos(k*y);
46 
47  return RealGradient(ux, uy);
48  }
libMesh::RealGradient
RealVectorValue RealGradient
Definition: hp_coarsentest.h:49
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ operator()() [2/4]

RealGradient DivGradExactSolution::operator() ( Real  x,
Real  y 
)
inline

Definition at line 42 of file div_grad_exact_solution.h.

References libMesh::pi, and libMesh::Real.

43  {
44  const Real ux = .5*pi*sin(.5*pi*x)*sin(.5*pi*y);
45  const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y);
46 
47  return RealGradient(ux, uy);
48  }
libMesh::RealGradient
RealVectorValue RealGradient
Definition: hp_coarsentest.h:49
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

◆ operator()() [3/4]

RealGradient DivGradExactSolution::operator() ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 50 of file div_grad_exact_solution.h.

References libMesh::pi, and libMesh::Real.

51  {
52  const Real ux = .5*pi*sin(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
53  const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
54  const Real uz = .5*pi*cos(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
55 
56  return RealGradient(ux, uy, uz);
57  }
libMesh::RealGradient
RealVectorValue RealGradient
Definition: hp_coarsentest.h:49
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

◆ operator()() [4/4]

RealGradient DivGradExactSolution::operator() ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 50 of file div_grad_exact_solution.h.

References libMesh::Real.

51  {
52  const Real ux = k*sin(k*x)*sin(k*y)*cos(k*z);
53  const Real uy = -k*cos(k*x)*cos(k*y)*cos(k*z);
54  const Real uz = k*cos(k*x)*sin(k*y)*sin(k*z);
55 
56  return RealGradient(ux, uy, uz);
57  }
libMesh::RealGradient
RealVectorValue RealGradient
Definition: hp_coarsentest.h:49
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:144

◆ scalar() [1/4]

Real DivGradExactSolution::scalar ( Real  x,
Real  y 
)
inline

Definition at line 32 of file div_grad_exact_solution.h.

References libMesh::pi.

33  {
34  return cos(.5*pi*x)*sin(.5*pi*y);
35  }
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

◆ scalar() [2/4]

Real DivGradExactSolution::scalar ( Real  x,
Real  y 
)
inline

Definition at line 32 of file div_grad_exact_solution.h.

Referenced by assemble_divgrad(), and fe_assembly().

33  {
34  return cos(k*x)*sin(k*y);
35  }

◆ scalar() [3/4]

Real DivGradExactSolution::scalar ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 37 of file div_grad_exact_solution.h.

38  {
39  return cos(k*x)*sin(k*y)*cos(k*z);
40  }

◆ scalar() [4/4]

Real DivGradExactSolution::scalar ( Real  x,
Real  y,
Real  z 
)
inline

Definition at line 37 of file div_grad_exact_solution.h.

References libMesh::pi.

38  {
39  return cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
40  }
libMesh::pi
const Real pi
.
Definition: libmesh.h:299

Member Data Documentation

◆ k

const Real DivGradExactSolution::k = .5*pi
private

Definition at line 112 of file div_grad_exact_solution.h.

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