Q1HexahedronFiniteElement Class Reference

#include <Q1HexahedronFiniteElement.hpp>

Inheritance diagram for Q1HexahedronFiniteElement:

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List of all members.

Public Types

enum  {
  numberOfDegreesOfFreedom = 8, numberOfVertexDegreesOfFreedom = 1, numberOfEdgeDegreesOfFreedom = 0, numberOfFaceDegreesOfFreedom = 0,
  numberOfVolumeDegreesOfFreedom = 0, numberOfFaceLivingDegreesOfFreedom = 4
}
enum  
typedef
QuadratureFormulaQ1Hexahedron 		QuadratureType
typedef TinyVector
< numberOfDegreesOfFreedom > 		ElementaryVector
typedef TinyMatrix
< numberOfDegreesOfFreedom,
numberOfDegreesOfFreedom > 		ElementaryMatrix

Public Member Functions

real_t W (const size_t &i, const TinyVector< 3 > &x) const
real_t dxW (const size_t &i, const TinyVector< 3 > &x) const
real_t dyW (const size_t &i, const TinyVector< 3 > &x) const
real_t dzW (const size_t &i, const TinyVector< 3 > &x) const
const TinyVector
< QuadratureType::numberOfQuadraturePoints,
TinyVector< 3 > > & 		integrationVertices () const
 Q1HexahedronFiniteElement ()
 ~Q1HexahedronFiniteElement ()
const real_t & W (const size_t &i, const size_t &j) const
const real_t & dxW (const size_t &i, const size_t &j) const
const real_t & dyW (const size_t &i, const size_t &j) const
const real_t & dzW (const size_t &i, const size_t &j) const
void integrateWjWi (ElementaryMatrix &matElem, const ConformTransformation &T) const
void integrateDWjWi (ElementaryMatrix &matElem, const size_t &n, const ConformTransformation &T) const
void integrateWjDWi (ElementaryMatrix &matElem, const size_t &n, const ConformTransformation &T) const
void integrateDWjDWi (ElementaryMatrix &matElem, const size_t &n, const size_t &m, const ConformTransformation &T) const
void integrateWj (ElementaryVector &vectElem, const ConformTransformation &T, const TinyVector< numberOfQuadraturePoints, real_t > &f) const

Static Public Member Functions

static const TinyVector
< 3, real_t > & 		massCenter ()
static Q1HexahedronFiniteElement & instance ()
static void create ()
static void destroy ()

Static Public Attributes

static const size_t facesDOF [Hexahedron::NumberOfFaces][numberOfFaceLivingDegreesOfFreedom]

Protected Member Functions

real_t __W (const size_t &i, const size_t &j)
real_t __dxW (const size_t &i, const size_t &j)
real_t __dyW (const size_t &i, const size_t &j)
real_t __dzW (const size_t &i, const size_t &j)

Protected Attributes

TinyMatrix
< numberOfDegreesOfFreedom,
numberOfQuadraturePoints > 		__w
TinyMatrix
< numberOfDegreesOfFreedom,
numberOfQuadraturePoints > 		__dxw
TinyMatrix
< numberOfDegreesOfFreedom,
numberOfQuadraturePoints > 		__dyw
TinyMatrix
< numberOfDegreesOfFreedom,
numberOfQuadraturePoints > 		__dzw

Static Protected Attributes

static Q1HexahedronFiniteElement * __pInstance

Static Private Attributes

static TinyVector< 3, real_t > __massCenter

Detailed Description

Definition at line 32 of file Q1HexahedronFiniteElement.hpp.

Member Typedef Documentation

typedef QuadratureFormulaQ1Hexahedron LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::QuadratureType [inherited]

default quadrature type

Definition at line 46 of file LagrangianFiniteElement.hpp.

typedef TinyVector<numberOfDegreesOfFreedom> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::ElementaryVector [inherited]

type of elementary vector

Definition at line 54 of file LagrangianFiniteElement.hpp.

typedef TinyMatrix<numberOfDegreesOfFreedom, numberOfDegreesOfFreedom> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::ElementaryMatrix [inherited]

type of elementary matrix

Definition at line 59 of file LagrangianFiniteElement.hpp.

Member Enumeration Documentation

anonymous enum

Enumerator:
numberOfDegreesOfFreedom 
numberOfVertexDegreesOfFreedom 
numberOfEdgeDegreesOfFreedom 
numberOfFaceDegreesOfFreedom 
numberOfVolumeDegreesOfFreedom 
numberOfFaceLivingDegreesOfFreedom 

Definition at line 41 of file Q1HexahedronFiniteElement.hpp.

00041        {
00042     numberOfDegreesOfFreedom = 8,
00043     numberOfVertexDegreesOfFreedom = 1,
00044     numberOfEdgeDegreesOfFreedom = 0,
00045     numberOfFaceDegreesOfFreedom = 0,
00046     numberOfVolumeDegreesOfFreedom = 0,
00047     numberOfFaceLivingDegreesOfFreedom = 4 // degrees of freedom carried by a face
00048   };

anonymous enum [inherited]

Definition at line 48 of file LagrangianFiniteElement.hpp.

00048        {
00049     numberOfQuadraturePoints = QuadratureType::numberOfQuadraturePoints
00050   };

Constructor & Destructor Documentation

Q1HexahedronFiniteElement::Q1HexahedronFiniteElement (  )  [inline]

Definition at line 113 of file Q1HexahedronFiniteElement.hpp.

00114   {
00115     ;
00116   }

Q1HexahedronFiniteElement::~Q1HexahedronFiniteElement (  )  [inline]

Definition at line 118 of file Q1HexahedronFiniteElement.hpp.

00119   {
00120     ;
00121   }

Member Function Documentation

static const TinyVector<3, real_t>& Q1HexahedronFiniteElement::massCenter (  )  [inline, static]

returns the mass center of the reference element

Returns:
__massCenter

Definition at line 60 of file Q1HexahedronFiniteElement.hpp.

References __massCenter.

00061   {
00062     return __massCenter;
00063   }

real_t Q1HexahedronFiniteElement::W ( const size_t &  i,
const TinyVector< 3 > &  x 
) const

Computes a hat function at a given point

Parameters:
i the hat function number
x the evaluation point
Returns:
$ w_i(\mathbf{x}) $

Definition at line 35 of file Q1HexahedronFiniteElement.cpp.

References ErrorHandler::unexpected.

00036 {
00037   const real_t& x = X[0];
00038   const real_t& y = X[1];
00039   const real_t& z = X[2];
00040 
00041   switch (i) {
00042   case 0: {
00043     return (1-x)*(1-y)*(1-z);
00044   }
00045   case 1: {
00046     return x*(1-y)*(1-z);
00047   }
00048   case 2: {
00049     return x*y*(1-z);
00050   }
00051   case 3: {
00052     return (1-x)*y*(1-z);
00053   }
00054   case 4: {
00055     return (1-x)*(1-y)*z;
00056   }
00057   case 5: {
00058     return x*(1-y)*z;
00059   }
00060   case 6: {
00061     return x*y*z;
00062   }
00063   case 7: {
00064     return (1-x)*y*z;
00065   }
00066   default: {
00067     throw ErrorHandler(__FILE__,__LINE__,
00068                        "unexpected basis function number",
00069                        ErrorHandler::unexpected);
00070     return 0.;
00071   }
00072   }
00073 }

real_t Q1HexahedronFiniteElement::dxW ( const size_t &  i,
const TinyVector< 3 > &  x 
) const

Computes a hat function derivative at a given point

Parameters:
i the hat function number
x the evaluation point
Returns:
$ \partial_x w_i(\mathbf{x}) $

Definition at line 76 of file Q1HexahedronFiniteElement.cpp.

References ErrorHandler::unexpected.

00077 {
00078   const real_t& y = X[1];
00079   const real_t& z = X[2];
00080 
00081   switch (i) {
00082   case 0: {
00083     return -(1-y)*(1-z);
00084   }
00085   case 1: {
00086     return (1-y)*(1-z);
00087   }
00088   case 2: {
00089     return y*(1-z);
00090   }
00091   case 3: {
00092     return -y*(1-z);
00093   }
00094   case 4: {
00095     return -(1-y)*z;
00096   }
00097   case 5: {
00098     return (1-y)*z;
00099   }
00100   case 6: {
00101     return y*z;
00102   }
00103   case 7: {
00104     return -y*z;
00105   }
00106   default: {
00107     throw ErrorHandler(__FILE__,__LINE__,
00108                        "unexpected basis function number",
00109                        ErrorHandler::unexpected);
00110     return 0.;
00111   }
00112   }
00113 }

real_t Q1HexahedronFiniteElement::dyW ( const size_t &  i,
const TinyVector< 3 > &  x 
) const

Computes a hat function derivative at a given point

Parameters:
i the hat function number
x the evaluation point
Returns:
$ \partial_y w_i(\mathbf{x}) $

Definition at line 116 of file Q1HexahedronFiniteElement.cpp.

References ErrorHandler::unexpected.

00117 {
00118   const real_t& x = X[0];
00119   const real_t& z = X[2];
00120 
00121   switch (i) {
00122   case 0: {
00123     return (1-x)*-(1-z);
00124   }
00125   case 1: {
00126     return x*-(1-z);
00127   }
00128   case 2: {
00129     return x*(1-z);
00130   }
00131   case 3: {
00132     return (1-x)*(1-z);
00133   }
00134   case 4: {
00135     return (1-x)*-z;
00136   }
00137   case 5: {
00138     return x*-z;
00139   }
00140   case 6: {
00141     return x*z;
00142   }
00143   case 7: {
00144     return (1-x)*z;
00145   }
00146   default: {
00147     throw ErrorHandler(__FILE__,__LINE__,
00148                        "unexpected basis function number",
00149                        ErrorHandler::unexpected);
00150     return 0.;
00151   }
00152   }
00153 }

real_t Q1HexahedronFiniteElement::dzW ( const size_t &  i,
const TinyVector< 3 > &  x 
) const

Computes a hat function derivative at a given point

Parameters:
i the hat function number
x the evaluation point
Returns:
$ \partial_z w_i(\mathbf{x}) $

Definition at line 156 of file Q1HexahedronFiniteElement.cpp.

References ErrorHandler::unexpected.

00157 {
00158   const real_t& x = X[0];
00159   const real_t& y = X[1];
00160 
00161   switch (i) {
00162   case 0: {
00163     return -(1-x)*(1-y);
00164   }
00165   case 1: {
00166     return -x*(1-y);
00167   }
00168   case 2: {
00169     return -x*y;
00170   }
00171   case 3: {
00172     return -(1-x)*y;
00173   }
00174   case 4: {
00175     return (1-x)*(1-y);
00176   }
00177   case 5: {
00178     return x*(1-y);
00179   }
00180   case 6: {
00181     return x*y;
00182   }
00183   case 7: {
00184     return (1-x)*y;
00185   }
00186   default: {
00187     throw ErrorHandler(__FILE__,__LINE__,
00188                        "unexpected basis function number",
00189                        ErrorHandler::unexpected);
00190     return 0.;
00191   }
00192   }
00193 }

const TinyVector<QuadratureType::numberOfQuadraturePoints, TinyVector<3> >& Q1HexahedronFiniteElement::integrationVertices (  )  const [inline]

Definition at line 108 of file Q1HexahedronFiniteElement.hpp.

References StaticBase< QuadratureFormulaQ1Hexahedron >::instance(), and QuadratureFormulaQ1Hexahedron::vertices().

00109   {
00110     return QuadratureType::instance().vertices();
00111   }

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static Q1HexahedronFiniteElement & StaticBase< Q1HexahedronFiniteElement >::instance (  )  [inline, static, inherited]

Access to auto instanciated static;

Returns:
*__pInstance

Definition at line 46 of file StaticBase.hpp.

00047   {
00048     return *__pInstance;
00049   }

static void StaticBase< Q1HexahedronFiniteElement >::create (  )  [inline, static, inherited]

Creates __pInstance in Embedding class.

Definition at line 55 of file StaticBase.hpp.

Referenced by ThreadStaticCenter::ThreadStaticCenter().

00056   {
00057     __pInstance = new EmbeddingClass();
00058   }

static void StaticBase< Q1HexahedronFiniteElement >::destroy (  )  [inline, static, inherited]

Destroyes __autoInstanciated in Embedding class.

Definition at line 64 of file StaticBase.hpp.

Referenced by ThreadStaticCenter::~ThreadStaticCenter().

00065   {
00066     delete __pInstance;
00067   }

real_t LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__W ( const size_t &  i,
const size_t &  j 
) [inline, protected, inherited]

Computes hat function value at quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function value

Definition at line 81 of file LagrangianFiniteElement.hpp.

00082   {
00083     return self().W(i,self().integrationVertices()[j]);
00084   }

real_t LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dxW ( const size_t &  i,
const size_t &  j 
) [inline, protected, inherited]

Computes hat function derivative by x at quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's derivative value

Definition at line 94 of file LagrangianFiniteElement.hpp.

00095   {
00096     return self().dxW(i,self().integrationVertices()[j]);
00097   }

real_t LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dyW ( const size_t &  i,
const size_t &  j 
) [inline, protected, inherited]

Computes hat function derivative by y at quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's derivative value

Definition at line 107 of file LagrangianFiniteElement.hpp.

00108   {
00109     return self().dyW(i,self().integrationVertices()[j]);
00110   }

real_t LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dzW ( const size_t &  i,
const size_t &  j 
) [inline, protected, inherited]

Computes hat function derivative by z at quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's derivative value

Definition at line 120 of file LagrangianFiniteElement.hpp.

00121   {
00122     return self().dzW(i,self().integrationVertices()[j]);
00123   }

const real_t& LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::W ( const size_t &  i,
const size_t &  j 
) const [inline, inherited]

Read-only access to hat function value at a quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's value

Definition at line 147 of file LagrangianFiniteElement.hpp.

00148   {
00149     return __w(i,j);
00150   }

const real_t& LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::dxW ( const size_t &  i,
const size_t &  j 
) const [inline, inherited]

Read-only access to hat function's derivative by x value at a quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's value

Definition at line 161 of file LagrangianFiniteElement.hpp.

00162   {
00163     return __dxw(i,j);
00164   }

const real_t& LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::dyW ( const size_t &  i,
const size_t &  j 
) const [inline, inherited]

Read-only access to hat function's derivative by y value at a quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's value

Definition at line 175 of file LagrangianFiniteElement.hpp.

00176   {
00177     return __dyw(i,j);
00178   }

const real_t& LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::dzW ( const size_t &  i,
const size_t &  j 
) const [inline, inherited]

Read-only access to hat function's derivative by z value at a quadrature point

Parameters:
i the hat function number
j the number of quadrature point
Returns:
the function's value

Definition at line 189 of file LagrangianFiniteElement.hpp.

00190   {
00191     return __dzw(i,j);
00192   }

void LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::integrateWjWi ( ElementaryMatrix &  matElem,
const ConformTransformation &  T 
) const [inline, inherited]

Computes elementary matrix associated to $ \int w_j w_i $ on a given element using the associated conform transformation

Parameters:
matElem the elementary matrix
T the given transformation

Definition at line 203 of file LagrangianFiniteElement.hpp.

00205   {
00206     ElementaryMatrix tmp = 0;
00207 
00208     for (size_t k=0; k<numberOfQuadraturePoints; ++k) { // Loop on integration vertices
00209       for (size_t j=0; j<numberOfDegreesOfFreedom; ++j) {
00210         for (size_t i=0; i<=j; ++i) {
00211           tmp(i,j)
00212             += W(i,k) * W(j,k) * QuadratureType::instance().weight(k);
00213         }
00214       }
00215     }
00216 
00217     // for this operator, matElem is symetric.
00218     for (size_t j=0; j<numberOfDegreesOfFreedom; ++j)
00219       for (size_t i=j+1; i<numberOfDegreesOfFreedom; ++i)
00220         tmp(i,j) = tmp(j,i);
00221 
00222     matElem += tmp;
00223   }

void LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::integrateDWjWi ( ElementaryMatrix &  matElem,
const size_t &  n,
const ConformTransformation &  T 
) const [inline, inherited]

Computes elementary matrix associated to $ \int \partial_{x_n} w_j w_i $ on a given element using the associated conform transformation

Parameters:
matElem the elementary matrix
n the $ n $ in $ \partial_{x_n} $
T the given transformation

Definition at line 235 of file LagrangianFiniteElement.hpp.

00238   {
00239     ElementaryMatrix tmp = 0;
00240 
00241     for (size_t k=0; k<numberOfQuadraturePoints; ++k) { // Loop on integration vertices
00242       for (size_t j=0; j<numberOfDegreesOfFreedom; ++j) {
00243         const real_t fj
00244           = dxW(j,k)*T.invJacobian(0,n)
00245           + dyW(j,k)*T.invJacobian(1,n)
00246           + dzW(j,k)*T.invJacobian(2,n);
00247         for (size_t i=0; i<numberOfDegreesOfFreedom; ++i) {
00248           tmp(i,j)
00249             += fj * W(i,k)  * QuadratureType::instance().weight(k);
00250         }
00251       }
00252     }
00253     matElem += tmp;
00254   }

void LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::integrateWjDWi ( ElementaryMatrix &  matElem,
const size_t &  n,
const ConformTransformation &  T 
) const [inline, inherited]

Computes elementary matrix associated to $ \int w_j \partial_{x_n} w_i $ on a given element using the associated conform transformation

Parameters:
matElem the elementary matrix
n the $ n $ in $ \partial_{x_n} $
T the given transformation

Definition at line 266 of file LagrangianFiniteElement.hpp.

00269   {
00270     ElementaryMatrix tmp = 0;
00271 
00272     for (size_t k=0; k<numberOfQuadraturePoints; ++k) { // Loop on integration vertices
00273       for (size_t i=0; i<numberOfDegreesOfFreedom; ++i) {
00274         const real_t fi
00275           = dxW(i,k)*T.invJacobian(0,n)
00276           + dyW(i,k)*T.invJacobian(1,n)
00277           + dzW(i,k)*T.invJacobian(2,n);
00278         for (size_t j=0; j<numberOfDegreesOfFreedom; ++j) {
00279           tmp(i,j)
00280             += fi * W(j,k) * QuadratureType::instance().weight(k);
00281         }
00282       }
00283     }
00284     matElem += tmp;
00285   }

void LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::integrateDWjDWi ( ElementaryMatrix &  matElem,
const size_t &  n,
const size_t &  m,
const ConformTransformation &  T 
) const [inline, inherited]

Computes elementary matrix associated to $ \int \partial_{x_n} w_j \partial_{x_m} w_i $ on a given element using the associated conform transformation

Parameters:
matElem the elementary matrix
n the $ n $ in $ \partial_{x_n} $
m the $ m $ in $ \partial_{x_m} $
T the given transformation

Definition at line 298 of file LagrangianFiniteElement.hpp.

00302   {
00303     ElementaryMatrix tmp = 0;
00304 
00305     for (size_t k=0; k<numberOfQuadraturePoints; ++k) { // Loop on integration vertices
00306       for (size_t j=0; j<numberOfDegreesOfFreedom; ++j) {
00307         const real_t fj
00308           = dxW(j,k)*T.invJacobian(0,n)
00309           + dyW(j,k)*T.invJacobian(1,n)
00310           + dzW(j,k)*T.invJacobian(2,n);
00311         for (size_t i=0; i<numberOfDegreesOfFreedom; ++i) {
00312           tmp(i,j)
00313             += fj
00314             * (  dxW(i,k)*T.invJacobian(0,m)
00315                + dyW(i,k)*T.invJacobian(1,m)
00316                + dzW(i,k)*T.invJacobian(2,m) )
00317             * QuadratureType::instance().weight(k);
00318         }
00319       }
00320     }
00321 
00322     matElem += tmp;
00323   }

void LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::integrateWj ( ElementaryVector &  vectElem,
const ConformTransformation &  T,
const TinyVector< numberOfQuadraturePoints, real_t > &  f 
) const [inline, inherited]

Computes elementary vector associated to $ \int f w_i $ on a given element using the associated conform transformation

Parameters:
vectElem the elementary vector
T the given transformation
f $ f $ values at quadrature points

Definition at line 334 of file LagrangianFiniteElement.hpp.

00337   {
00338     vectElem = 0;
00339 
00340     for (size_t k=0; k<numberOfQuadraturePoints; ++k)
00341       for (size_t j=0; j<numberOfDegreesOfFreedom; ++j) {
00342         vectElem[j]
00343           += W(j,k)
00344           *  f[k]
00345           *  QuadratureType::instance().weight(k);
00346       }
00347   }

Member Data Documentation

TinyVector< 3, real_t > Q1HexahedronFiniteElement::__massCenter [static, private]

mass center of the reference element

Definition at line 38 of file Q1HexahedronFiniteElement.hpp.

Referenced by massCenter().

const size_t Q1HexahedronFiniteElement::facesDOF [static]

Initial value:

 {{ 0, 1, 2, 3},
   { 0, 1, 4, 5},
   { 1, 2, 5, 6},
   { 2, 3, 6, 7},
   { 0, 3, 4, 7},
   { 4, 5, 6, 7}}
Degrees of freedom living on faces

Definition at line 53 of file Q1HexahedronFiniteElement.hpp.

Q1HexahedronFiniteElement * StaticBase< Q1HexahedronFiniteElement >::__pInstance [static, protected, inherited]

The static variable

Definition at line 37 of file StaticBase.hpp.

TinyMatrix<numberOfDegreesOfFreedom,numberOfQuadraturePoints> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__w [protected, inherited]

hat function values at quadrature points

Definition at line 127 of file LagrangianFiniteElement.hpp.

TinyMatrix<numberOfDegreesOfFreedom,numberOfQuadraturePoints> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dxw [protected, inherited]

hat function dx values at quadrature points

Definition at line 130 of file LagrangianFiniteElement.hpp.

TinyMatrix<numberOfDegreesOfFreedom,numberOfQuadraturePoints> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dyw [protected, inherited]

hat function dy values at quadrature points

Definition at line 133 of file LagrangianFiniteElement.hpp.

TinyMatrix<numberOfDegreesOfFreedom,numberOfQuadraturePoints> LagrangianFiniteElement< numberOfDegreesOfFreedom, Q1HexahedronFiniteElement , QuadratureFormulaQ1Hexahedron >::__dzw [protected, inherited]

hat function dz values at quadrature points

Definition at line 136 of file LagrangianFiniteElement.hpp.

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