v0.14.0
Static Public Member Functions | List of all members
ApproxFunctions Struct Reference

Static Public Member Functions

static FTensor::Tensor1< double, BASE_DIM > fUn (const double x, const double y, double z)
 
static FTensor::Tensor2< double, BASE_DIM, SPACE_DIM > diffFun (const double x, const double y)
 
static FTensor::Tensor3< double, BASE_DIM, SPACE_DIM, SPACE_DIM > diff2Fun (const double x, const double y)
 
static FTensor::Tensor1< double, BASE_DIM > fUn (const double x, const double y, double z)
 
static FTensor::Tensor2< double, BASE_DIM, SPACE_DIM > diffFun (const double x, const double y, const double z)
 

Detailed Description

Examples
hcurl_check_approx_in_2d.cpp, hdiv_check_approx_in_3d.cpp, and scalar_check_approximation.cpp.

Definition at line 44 of file hcurl_check_approx_in_2d.cpp.

Member Function Documentation

◆ diff2Fun()

static FTensor::Tensor3<double, BASE_DIM, SPACE_DIM, SPACE_DIM> ApproxFunctions::diff2Fun ( const double  x,
const double  y 
)
inlinestatic
Examples
hcurl_check_approx_in_2d.cpp.

Definition at line 92 of file hcurl_check_approx_in_2d.cpp.

92  {
93  return FTensor::Tensor3<double, BASE_DIM, SPACE_DIM, SPACE_DIM>(
94  // x,xx 0/000
95 
96  30 * 4 * a6 * pow(x, 3) * pow(y, 0) +
97  20 * 3 * a5 * pow(x, 2) * pow(y, 1) +
98  12 * 2 * a4 * pow(x, 1) * pow(y, 2) +
99  6 * 1 * a3 * pow(x, 0) * pow(y, 3),
100 
101  // x,xy 1/001
102 
103  20 * 1 * a5 * pow(x, 3) * pow(y, 0) +
104  12 * 2 * a4 * pow(x, 2) * pow(y, 2) +
105  6 * 3 * a3 * pow(x, 1) * pow(y, 2) +
106  2 * 4 * a2 * pow(x, 0) * pow(y, 3),
107 
108  // x,yx 2/010
109 
110  5 * 4 * a5 * pow(x, 3) * pow(y, 0) +
111  8 * 3 * a4 * pow(x, 2) * pow(y, 1) +
112  9 * 2 * a3 * pow(x, 1) * pow(y, 2) +
113  8 * 1 * a2 * pow(x, 0) * pow(y, 3),
114 
115  // x,yy 3/011
116 
117  8 * 1 * a4 * pow(x, 3) * pow(y, 0) +
118  9 * 2 * a3 * pow(x, 2) * pow(y, 1) +
119  8 * 3 * a2 * pow(x, 1) * pow(y, 2) +
120  5 * 4 * a1 * pow(x, 0) * pow(y, 3),
121 
122  // y,xx 4/100
123 
124  5 * 4 * a5 * pow(x, 3) * pow(y, 0) +
125  8 * 3 * a4 * pow(x, 2) * pow(y, 1) +
126  9 * 2 * a3 * pow(x, 1) * pow(y, 2) +
127  8 * 1 * a2 * pow(x, 0) * pow(y, 3),
128 
129  // y,xy 5/101
130 
131  8 * 1 * a4 * pow(x, 3) * pow(y, 0) +
132  9 * 2 * a3 * pow(x, 2) * pow(y, 1) +
133  8 * 3 * a2 * pow(x, 1) * pow(y, 2) +
134  5 * 4 * a1 * pow(x, 0) * pow(y, 3),
135 
136  // y,yx 6/110
137 
138  2 * 4 * a4 * pow(x, 3) * pow(y, 0) +
139  6 * 3 * a3 * pow(x, 2) * pow(y, 1) +
140  12 * 2 * a2 * pow(x, 1) * pow(y, 2) +
141  20 * 1 * a1 * pow(x, 0) * pow(y, 3),
142 
143  // y,yy 7/111
144 
145  6 * 1 * a3 * pow(x, 3) * pow(y, 0) +
146  12 * 2 * a2 * pow(x, 2) * pow(y, 1) +
147  20 * 3 * a1 * pow(x, 1) * pow(y, 2) +
148  30 * 4 * a0 * pow(x, 0) * pow(y, 3),
149 
150  // z,xx 8/200
151  0.,
152  // z,xy 9/201
153  0.,
154  // z,yx 10/210
155  0.,
156  // z,yy 11/211
157  0.);
158  }

◆ diffFun() [1/2]

static FTensor::Tensor2<double, BASE_DIM, SPACE_DIM> ApproxFunctions::diffFun ( const double  x,
const double  y 
)
inlinestatic
Examples
hcurl_check_approx_in_2d.cpp, hdiv_check_approx_in_3d.cpp, and scalar_check_approximation.cpp.

Definition at line 68 of file hcurl_check_approx_in_2d.cpp.

69  {
70  return FTensor::Tensor2<double, BASE_DIM, SPACE_DIM>(
71  // x,x
72  30 * a6 * pow(x, 4) * pow(y, 0) + 20 * a5 * pow(x, 3) * pow(y, 1) +
73  12 * a4 * pow(x, 2) * pow(y, 2) + 6 * a3 * pow(x, 1) * pow(y, 3) +
74  2 * a2 * pow(x, 0) * pow(y, 4),
75  // x,y
76  5 * a5 * pow(x, 4) * pow(y, 0) + 8 * a4 * pow(x, 3) * pow(y, 1) +
77  9 * a3 * pow(x, 2) * pow(y, 2) + 8 * a2 * pow(x, 1) * pow(y, 3) +
78  5 * a1 * pow(x, 0) * pow(y, 4),
79  // y,x
80  5 * a5 * pow(x, 4) * pow(y, 0) + 8 * a4 * pow(x, 3) * pow(y, 1) +
81  9 * a3 * pow(x, 2) * pow(y, 2) + 8 * a2 * pow(x, 1) * pow(y, 3) +
82  5 * a1 * pow(x, 0) * pow(y, 4),
83  // y,y
84  2 * a4 * pow(x, 4) * pow(y, 0) + 6 * a3 * pow(x, 3) * pow(y, 1) +
85  12 * a2 * pow(x, 2) * pow(y, 2) + 20 * a1 * pow(x, 1) * pow(y, 3) +
86  30 * a0 * pow(x, 0) * pow(y, 4),
87  // z
88  0., 0.);
89  }

◆ diffFun() [2/2]

static FTensor::Tensor2<double, BASE_DIM, SPACE_DIM> ApproxFunctions::diffFun ( const double  x,
const double  y,
const double  z 
)
inlinestatic

Definition at line 56 of file hdiv_check_approx_in_3d.cpp.

56  {
57  return FTensor::Tensor2<double, BASE_DIM, SPACE_DIM>(
58  // x,x
59  1. + 3 * x * x,
60  // x,y
61  2. * y,
62  // x, z
63  0.,
64  // y,x
65  z,
66  // y,y
67  1. + 3 * y * y,
68  // y,z
69  x,
70  // z
71  2 * x, 0., 1. + 3 * z * z);
72  }

◆ fUn() [1/2]

static FTensor::Tensor1<double, BASE_DIM> ApproxFunctions::fUn ( const double  x,
const double  y,
double  z 
)
inlinestatic

Definition at line 44 of file hdiv_check_approx_in_3d.cpp.

45  {
46  return FTensor::Tensor1<double, BASE_DIM>(
47  // x
48  x + y*y + x*x*x,
49  // y
50  y + z*x + y*y*y,
51  // z
52  z + x*x + z*z*z);
53  }

◆ fUn() [2/2]

static FTensor::Tensor1<double, BASE_DIM> ApproxFunctions::fUn ( const double  x,
const double  y,
double  z 
)
inlinestatic
Examples
hcurl_check_approx_in_2d.cpp, hdiv_check_approx_in_3d.cpp, and scalar_check_approximation.cpp.

Definition at line 46 of file hcurl_check_approx_in_2d.cpp.

47  {
48  return FTensor::Tensor1<double, BASE_DIM>(
49  // x
50  6 * a6 * std::pow(x, 5) * std::pow(y, 0) +
51  5 * a5 * std::pow(x, 4) * std::pow(y, 1) +
52  4 * a4 * std::pow(x, 3) * std::pow(y, 2) +
53  3 * a3 * std::pow(x, 2) * std::pow(y, 3) +
54  2 * a2 * std::pow(x, 1) * std::pow(y, 4) +
55  1 * a1 * std::pow(x, 0) * std::pow(y, 5),
56  // y
57  1 * a5 * std::pow(x, 5) * std::pow(y, 0) +
58  2 * a4 * std::pow(x, 4) * std::pow(y, 1) +
59  3 * a3 * std::pow(x, 3) * std::pow(y, 2) +
60  4 * a2 * std::pow(x, 2) * std::pow(y, 3) +
61  5 * a1 * std::pow(x, 1) * std::pow(y, 4) +
62  6 * a0 * std::pow(x, 0) * std::pow(y, 5),
63 
64  // z
65  0.);
66  }
The documentation for this struct was generated from the following files:
a2
constexpr double a2
Definition: hcurl_check_approx_in_2d.cpp:39
a3
constexpr double a3
Definition: hcurl_check_approx_in_2d.cpp:40
FTensor::Tensor1
Definition: Tensor1_value.hpp:8
FTensor::Tensor2
Definition: Tensor2_value.hpp:16
FTensor::Tensor3
Definition: Tensor3_value.hpp:12
a1
constexpr double a1
Definition: hcurl_check_approx_in_2d.cpp:38
a4
constexpr double a4
Definition: hcurl_check_approx_in_2d.cpp:41
a6
constexpr double a6
Definition: hcurl_check_approx_in_2d.cpp:43
a0
constexpr double a0
Definition: hcurl_check_approx_in_2d.cpp:37
a5
constexpr double a5
Definition: hcurl_check_approx_in_2d.cpp:42
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