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Classes | Functions | Variables
fe_test.h File Reference

Go to the source code of this file.

Classes

class  SkewFunc
 
struct  Default
 
class  FETestBase< order, family, elem_type, build_nx, CaseName >
 
class  FETest< order, family, elem_type, CaseName >
 

Functions

Number linear_test (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Gradient linear_test_grad (const Point &, const Parameters &, const std::string &, const std::string &)
 
Number quadratic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Gradient quadratic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Number fe_cubic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Gradient fe_cubic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Number fe_quartic_test (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Gradient fe_quartic_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Number rational_test (const Point &p, const Parameters &, const std::string &, const std::string &)
 
Gradient rational_test_grad (const Point &p, const Parameters &, const std::string &, const std::string &)
 

Variables

static const Real rational_w = 0.75
 

Function Documentation

◆ fe_cubic_test()

Number fe_cubic_test ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 131 of file fe_test.h.

135{
136 const Real & x = p(0);
137 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
138 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
139
140 return x*(1-x)*(1-x) + x*x*(1-y) + x*(1-y)*(1-z) + y*(1-y)*z + z*(1-z)*(1-z);
141}
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition libmesh_common.h:144

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type, CaseName >::testU().

◆ fe_cubic_test_grad()

Gradient fe_cubic_test_grad ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 144 of file fe_test.h.

148{
149 const Real & x = p(0);
150 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
151 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
152
153 Gradient grad = 3*x*x-4*x+1 + 2*x*(1-y) + (1-y)*(1-z);
154 if (LIBMESH_DIM > 1)
155 grad(1) = -x*x - x*(1-z) + (1-2*y)*z;
156 if (LIBMESH_DIM > 2)
157 grad(2) = -x*(1-y) + y*(1-y) + 3*z*z-4*z+1;
158
159 return grad;
160}
libMesh::VectorValue
This class defines a vector in LIBMESH_DIM dimensional Real or Complex space.
Definition vector_value.h:48

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), and FETestBase< order, family, elem_type, build_nx, CaseName >::true_gradient().

◆ fe_quartic_test()

Number fe_quartic_test ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 164 of file fe_test.h.

168{
169 const Real & x = p(0);
170 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
171 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
172
173 return x*x*(1-x)*(1-x) + x*x*z*(1-y) + x*(1-x)*(1-y)*(1-z) + (1-x)*y*(1-y)*z + z*z*(1-z)*(1-z);
174}

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type, CaseName >::testU().

◆ fe_quartic_test_grad()

Gradient fe_quartic_test_grad ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 177 of file fe_test.h.

181{
182 const Real & x = p(0);
183 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
184 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
185
186 Gradient grad = 4*x*x*x-6*x*x+2*x + 2*x*z*(1-y) + (1-2*x)*(1-y)*(1-z) - y*(1-y)*z;
187 if (LIBMESH_DIM > 1)
188 grad(1) = -x*x*z - x*(1-x)*(1-z) + (1-x)*(1-2*y)*z;
189 if (LIBMESH_DIM > 2)
190 grad(2) = x*x*(1-y) - x*(1-x)*(1-y) + (1-x)*y*(1-y) + 4*z*z*z-6*z*z+2*z;
191
192 return grad;
193}

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), and FETestBase< order, family, elem_type, build_nx, CaseName >::true_gradient().

◆ linear_test()

Number linear_test ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 69 of file fe_test.h.

73{
74 const Real & x = p(0);
75 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
76 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
77
78 return x + 0.25*y + 0.0625*z;
79}

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp().

◆ linear_test_grad()

Gradient linear_test_grad ( const Point &  ,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 82 of file fe_test.h.

86{
87 Gradient grad = 1;
88 if (LIBMESH_DIM > 1)
89 grad(1) = 0.25;
90 if (LIBMESH_DIM > 2)
91 grad(2) = 0.0625;
92
93 return grad;
94}

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp().

◆ quadratic_test()

Number quadratic_test ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 98 of file fe_test.h.

102{
103 const Real & x = p(0);
104 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
105 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
106
107 return x*x + 0.5*y*y + 0.25*z*z + 0.125*x*y + 0.0625*x*z + 0.03125*y*z;
108}

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp().

◆ quadratic_test_grad()

Gradient quadratic_test_grad ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 111 of file fe_test.h.

115{
116 const Real & x = p(0);
117 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
118 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
119
120 Gradient grad = 2*x + 0.125*y + 0.0625*z;
121 if (LIBMESH_DIM > 1)
122 grad(1) = y + 0.125*x + 0.03125*z;
123 if (LIBMESH_DIM > 2)
124 grad(2) = 0.5*z + 0.0625*x + 0.03125*y;
125
126 return grad;
127}

References libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp().

◆ rational_test()

Number rational_test ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 203 of file fe_test.h.

207{
208 const Real & x = p(0);
209 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
210 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
211
212 const Real denom = ((1-x)*(1-x)+x*x+2*rational_w*x*(1-x))*
213 ((1-y)*(1-y)+y*y+2*rational_w*y*(1-y))*
214 ((1-z)*(1-z)+z*z+2*rational_w*z*(1-z));
215
216 return (x + 0.25*y + 0.0625*z)/denom;
217}
rational_w
static const Real rational_w
Definition fe_test.h:200

References rational_w, and libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), FESideTest< order, family, elem_type >::testU(), and FETest< order, family, elem_type, CaseName >::testU().

◆ rational_test_grad()

Gradient rational_test_grad ( const Point &  p,
const Parameters &  ,
const std::string &  ,
const std::string &   
)
inline

Definition at line 220 of file fe_test.h.

224{
225 const Real & x = p(0);
226 const Real & y = (LIBMESH_DIM > 1) ? p(1) : 0;
227 const Real & z = (LIBMESH_DIM > 2) ? p(2) : 0;
228
229 const Real xpoly = (1-x)*(1-x)+x*x+2*rational_w*x*(1-x);
230 const Real xderiv = -2*(1-x)+2*x+2*rational_w*(1-2*x);
231 const Real ypoly = (1-y)*(1-y)+y*y+2*rational_w*y*(1-y);
232 const Real yderiv = -2*(1-y)+2*y+2*rational_w*(1-2*y);
233 const Real zpoly = (1-z)*(1-z)+z*z+2*rational_w*z*(1-z);
234 const Real zderiv = -2*(1-z)+2*z+2*rational_w*(1-2*z);
235
236 const Real denom = xpoly * ypoly * zpoly;
237
238 const Real numer = (x + 0.25*y + 0.0625*z);
239
240 Gradient grad_n = 1, grad_d = xderiv * ypoly * zpoly;
241 if (LIBMESH_DIM > 1)
242 {
243 grad_n(1) = 0.25;
244 grad_d(1) = xpoly * yderiv * zpoly;
245 }
246 if (LIBMESH_DIM > 2)
247 {
248 grad_n(2) = 0.0625;
249 grad_d(2) = xpoly * ypoly * zderiv;
250 }
251
252 Gradient grad = (grad_n - numer * grad_d / denom) / denom;
253
254 return grad;
255}

References rational_w, and libMesh::Real.

Referenced by FETestBase< order, family, elem_type, build_nx, CaseName >::setUp(), and FETestBase< order, family, elem_type, build_nx, CaseName >::true_gradient().

Variable Documentation

◆ rational_w

const Real rational_w = 0.75
static

Definition at line 200 of file fe_test.h.

Referenced by rational_test(), rational_test_grad(), and FETestBase< order, family, elem_type, build_nx, CaseName >::setUp().

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