void
WallTensionEstimatorCylindricalCoordinates<Mesh >::constructGlobalStressVector()
{
//Creating the local stress tensors
VectorElemental elVecSigmaX (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
VectorElemental elVecSigmaY (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
VectorElemental elVecSigmaZ (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
LifeChrono chrono;
//Constructing the patch area vector for reconstruction purposes
solutionVect_Type patchArea (* (this->M_displacement), Unique, Add);
patchArea *= 0.0;
super::constructPatchAreaVector ( patchArea );
//Before assembling the reconstruction process is done
solutionVect_Type patchAreaR (patchArea, Repeated);
QuadratureRule fakeQuadratureRule;
Real refElemArea (0); //area of reference element
//compute the area of reference element
for (UInt iq = 0; iq < this->M_FESpace->qr().nbQuadPt(); iq++)
{
refElemArea += this->M_FESpace->qr().weight (iq);
}
Real wQuad (refElemArea / this->M_FESpace->refFE().nbDof() );
//Setting the quadrature Points = DOFs of the element and weight = 1
std::vector<GeoVector> coords = this->M_FESpace->refFE().refCoor();
std::vector<Real> weights (this->M_FESpace->fe().nbFEDof(), wQuad);
fakeQuadratureRule.setDimensionShape ( shapeDimension (this->M_FESpace->refFE().shape() ), this->M_FESpace->refFE().shape() );
fakeQuadratureRule.setPoints (coords, weights);
//Set the new quadrature rule
this->M_FESpace->setQuadRule (fakeQuadratureRule);
this->M_displayer->leaderPrint (" \n*********************************\n ");
this->M_displayer->leaderPrint (" Performing the analysis recovering the Cauchy stresses..., ", this->M_dataMaterial->solidType() );
this->M_displayer->leaderPrint (" \n*********************************\n ");
UInt totalDof = this->M_FESpace->dof().numTotalDof();
VectorElemental dk_loc (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
//Vectors for the deformation tensor
std::vector<matrix_Type> vectorDeformationF (this->M_FESpace->fe().nbFEDof(), * (this->M_deformationF) );
//Copying the displacement field into a vector with repeated map for parallel computations
solutionVect_Type dRep (* (this->M_displacement), Repeated);
chrono.start();
//Loop on each volume
for ( UInt i = 0; i < this->M_FESpace->mesh()->numVolumes(); ++i )
{
this->M_FESpace->fe().updateFirstDerivQuadPt ( this->M_FESpace->mesh()->volumeList ( i ) );
elVecSigmaX.zero();
elVecSigmaY.zero();
elVecSigmaZ.zero();
this->M_marker = this->M_FESpace->mesh()->volumeList ( i ).markerID();
UInt eleID = this->M_FESpace->fe().currentLocalId();
//Extracting the local displacement
for ( UInt iNode = 0; iNode < ( UInt ) this->M_FESpace->fe().nbFEDof(); iNode++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( iNode );
for ( UInt iComp = 0; iComp < this->M_FESpace->fieldDim(); ++iComp )
{
UInt ig = this->M_FESpace->dof().localToGlobalMap ( eleID, iloc ) + iComp * this->M_FESpace->dim() + this->M_offset;
dk_loc[iloc + iComp * this->M_FESpace->fe().nbFEDof()] = dRep[ig];
}
}
//Compute the element tensor F
AssemblyElementalStructure::computeLocalDeformationGradientWithoutIdentity ( dk_loc, vectorDeformationF, this->M_FESpace->fe() );
//Compute the local vector of the principal stresses
for ( UInt nDOF = 0; nDOF < ( UInt ) this->M_FESpace->fe().nbFEDof(); nDOF++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( nDOF );
vector_Type localDisplacement (this->M_FESpace->fieldDim(), 0.0);
for ( UInt coor = 0; coor < this->M_FESpace->fieldDim(); coor++ )
{
localDisplacement[coor] = iloc + coor * this->M_FESpace->fe().nbFEDof();
}
this->M_sigma->Scale (0.0);
this->M_firstPiola->Scale (0.0);
this->M_cofactorF->Scale (0.0);
this->M_deformationCylindricalF->Scale (0.0);
moveToCylindricalCoordinates (vectorDeformationF[nDOF], iloc, *M_deformationCylindricalF);
//Compute the rightCauchyC tensor
AssemblyElementalStructure::computeInvariantsRightCauchyGreenTensor (this->M_invariants, *M_deformationCylindricalF, * (this->M_cofactorF) );
//Compute the first Piola-Kirchhoff tensor
this->M_material->computeLocalFirstPiolaKirchhoffTensor (* (this->M_firstPiola), *M_deformationCylindricalF, * (this->M_cofactorF), this->M_invariants, this->M_marker);
//Compute the Cauchy tensor
AssemblyElementalStructure::computeCauchyStressTensor (* (this->M_sigma), * (this->M_firstPiola), this->M_invariants[3], *M_deformationCylindricalF);
//Assembling the local vectors for local tensions Component X
for ( int coor = 0; coor < this->M_FESpace->fieldDim(); coor++ )
{
(elVecSigmaX) [iloc + coor * this->M_FESpace->fe().nbFEDof()] = (* (this->M_sigma) ) (coor, 0);
}
//Assembling the local vectors for local tensions Component Y
for ( int coor = 0; coor < this->M_FESpace->fieldDim(); coor++ )
{
(elVecSigmaY) [iloc + coor * this->M_FESpace->fe().nbFEDof()] = (* (this->M_sigma) ) (coor, 1);
}
//Assembling the local vectors for local tensions Component Z
for ( int coor = 0; coor < this->M_FESpace->fieldDim(); coor++ )
{
(elVecSigmaZ) [iloc + coor * this->M_FESpace->fe().nbFEDof()] = (* (this->M_sigma) ) (coor, 2);
}
}
super::reconstructElementaryVector ( elVecSigmaX, patchAreaR, *this->M_FESpace );
super::reconstructElementaryVector ( elVecSigmaY, patchAreaR, *this->M_FESpace );
super::reconstructElementaryVector ( elVecSigmaZ, patchAreaR, *this->M_FESpace );
//Assembling the three elemental vector in the three global
for ( UInt ic = 0; ic < this->M_FESpace->fieldDim(); ++ic )
{
assembleVector (*this->M_sigmaX, elVecSigmaX, this->M_FESpace->fe(), this->M_FESpace->dof(), ic, this->M_offset + ic * totalDof );
assembleVector (*this->M_sigmaY, elVecSigmaY, this->M_FESpace->fe(), this->M_FESpace->dof(), ic, this->M_offset + ic * totalDof );
assembleVector (*this->M_sigmaZ, elVecSigmaZ, this->M_FESpace->fe(), this->M_FESpace->dof(), ic, this->M_offset + ic * totalDof );
}
}
this->M_sigmaX->globalAssemble();
this->M_sigmaY->globalAssemble();
this->M_sigmaZ->globalAssemble();
}
void
HyperbolicSolver< Mesh, SolverType >::
localEvolve ( const UInt& iElem )
{
// LAPACK wrapper of Epetra
Epetra_LAPACK lapack;
// Flags for LAPACK routines.
Int INFO[1] = { 0 };
Int NB = M_FESpace.refFE().nbDof();
// Parameter that indicate the Lower storage of matrices.
char param_L = 'L';
char param_N = 'N';
// Paramater that indicate the Transpose of matrices.
char param_T = 'T';
// Numbers of columns of the right hand side := 1.
Int NBRHS = 1;
// Clean the local flux
M_localFlux.zero();
// Loop on the faces of the element iElem and compute the local contribution
for ( UInt iFace (0); iFace < M_FESpace.mesh()->numLocalFaces(); ++iFace )
{
// Id mapping
const UInt iGlobalFace ( M_FESpace.mesh()->localFacetId ( iElem, iFace ) );
// Take the left element to the face, see regionMesh for the meaning of left element
const UInt leftElement ( M_FESpace.mesh()->faceElement ( iGlobalFace, 0 ) );
// Take the right element to the face, see regionMesh for the meaning of right element
const UInt rightElement ( M_FESpace.mesh()->faceElement ( iGlobalFace, 1 ) );
// Update the normal vector of the current face in each quadrature point
M_FESpace.feBd().updateMeasNormalQuadPt ( M_FESpace.mesh()->boundaryFacet ( iGlobalFace ) );
// Local flux of a face times the integration weight
VectorElemental localFaceFluxWeight ( M_FESpace.refFE().nbDof(), 1 );
// Solution in the left element
VectorElemental leftValue ( M_FESpace.refFE().nbDof(), 1 );
// Solution in the right element
VectorElemental rightValue ( M_FESpace.refFE().nbDof(), 1 );
// Extract the solution in the current element, now is the leftElement
extract_vec ( *M_uOld,
leftValue,
M_FESpace.refFE(),
M_FESpace.dof(),
leftElement , 0 );
// Check if the current face is a boundary face, that is rightElement == NotAnId
if ( !Flag::testOneSet ( M_FESpace.mesh()->face ( iGlobalFace ).flag(), EntityFlags::PHYSICAL_BOUNDARY | EntityFlags::SUBDOMAIN_INTERFACE ) )
{
// Extract the solution in the current element, now is the leftElement
extract_vec ( *M_uOld,
rightValue,
M_FESpace.refFE(),
M_FESpace.dof(),
rightElement , 0 );
}
else if ( Flag::testOneSet ( M_FESpace.mesh()->face ( iGlobalFace ).flag(), EntityFlags::SUBDOMAIN_INTERFACE ) )
{
// TODO: this works only for P0 elements
rightValue[ 0 ] = M_ghostDataMap[ iGlobalFace ];
}
else // Flag::testOneSet ( M_FESpace.mesh()->face ( iGlobalFace ).flag(), PHYSICAL_BOUNDARY )
{
// Clean the value of the right element
rightValue.zero();
// Check if the boundary conditions were updated.
if ( !M_BCh->bcUpdateDone() )
{
// Update the boundary conditions handler. We use the finite element of the boundary of the dual variable.
M_BCh->bcUpdate ( *M_FESpace.mesh(), M_FESpace.feBd(), M_FESpace.dof() );
}
// Take the boundary marker for the current boundary face
const ID faceMarker ( M_FESpace.mesh()->boundaryFacet ( iGlobalFace ).markerID() );
// Take the corrispective boundary function
const BCBase& bcBase ( M_BCh->findBCWithFlag ( faceMarker ) );
// Check if the bounday condition is of type Essential, useful for operator splitting strategies
if ( bcBase.type() == Essential )
{
// Loop on all the quadrature points
for ( UInt ig (0); ig < M_FESpace.feBd().nbQuadPt(); ++ig)
{
// Current quadrature point
KN<Real> quadPoint (3);
// normal vector
KN<Real> normal (3);
for (UInt icoor (0); icoor < 3; ++icoor)
{
quadPoint (icoor) = M_FESpace.feBd().quadPt ( ig, icoor );
normal (icoor) = M_FESpace.feBd().normal ( icoor, ig ) ;
}
// Compute the boundary contribution
rightValue[0] = bcBase ( M_data.dataTime()->time(), quadPoint (0), quadPoint (1), quadPoint (2), 0 );
const Real localFaceFlux = M_numericalFlux->firstDerivativePhysicalFluxDotNormal ( normal,
iElem,
M_data.dataTime()->time(),
quadPoint (0),
quadPoint (1),
quadPoint (2),
rightValue[ 0 ] );
// Update the local flux of the current face with the quadrature weight
localFaceFluxWeight[0] += localFaceFlux * M_FESpace.feBd().weightMeas ( ig );
}
}
else
{
/* If the boundary flag is not Essential then is automatically an outflow boundary.
We impose to localFaceFluxWeight a positive value. */
localFaceFluxWeight[0] = 1.;
}
// It is an outflow face, we use a ghost cell
if ( localFaceFluxWeight[0] > 1e-4 )
{
rightValue = leftValue;
}
// Clean the localFaceFluxWeight
localFaceFluxWeight.zero();
}
// Clean the localFaceFluxWeight
localFaceFluxWeight.zero();
// Loop on all the quadrature points
for ( UInt ig (0); ig < M_FESpace.feBd().nbQuadPt(); ++ig )
{
// Current quadrature point
KN<Real> quadPoint (3);
// normal vector
KN<Real> normal (3);
for (UInt icoor (0); icoor < 3; ++icoor)
{
quadPoint (icoor) = M_FESpace.feBd().quadPt ( ig, icoor );
normal (icoor) = M_FESpace.feBd().normal ( icoor, ig ) ;
}
// If the normal is orientated inward, we change its sign and swap the left and value of the solution
if ( iElem == rightElement )
{
normal *= -1.;
std::swap ( leftValue, rightValue );
}
const Real localFaceFlux = (*M_numericalFlux) ( leftValue[ 0 ],
rightValue[ 0 ],
normal,
iElem,
M_data.dataTime()->time(),
quadPoint (0),
quadPoint (1),
quadPoint (2) );
// Update the local flux of the current face with the quadrature weight
localFaceFluxWeight[0] += localFaceFlux * M_FESpace.feBd().weightMeas ( ig );
}
/* Put in localFlux the vector L^{-1} * localFlux
For more details see http://www.netlib.org/lapack/lapack-3.1.1/SRC/dtrtrs.f */
lapack.TRTRS ( param_L, param_N, param_N, NB, NBRHS, M_elmatMass[ iElem ].mat(), NB, localFaceFluxWeight, NB, INFO);
ASSERT_PRE ( !INFO[0], "Lapack Computation M_elvecSource = LB^{-1} rhs is not achieved." );
/* Put in localFlux the vector L^{-T} * localFlux
For more details see http://www.netlib.org/lapack/lapack-3.1.1/SRC/dtrtrs.f */
lapack.TRTRS ( param_L, param_T, param_N, NB, NBRHS, M_elmatMass[ iElem ].mat(), NB, localFaceFluxWeight, NB, INFO);
ASSERT_PRE ( !INFO[0], "Lapack Computation M_elvecSource = LB^{-1} rhs is not achieved." );
// Add to the local flux the local flux of the current face
M_localFlux += localFaceFluxWeight;
}
} // localEvolve
void
WallTensionEstimatorCylindricalCoordinates<Mesh >::analyzeTensionsRecoveryEigenvaluesCylindrical ( void )
{
LifeChrono chrono;
this->M_displayer->leaderPrint (" \n*********************************\n ");
this->M_displayer->leaderPrint (" Performing the analysis recovering the tensions..., ", this->M_dataMaterial->solidType() );
this->M_displayer->leaderPrint (" \n*********************************\n ");
solutionVect_Type patchArea (* (this->M_displacement), Unique, Add);
patchArea *= 0.0;
super::constructPatchAreaVector ( patchArea );
//Before assembling the reconstruction process is done
solutionVect_Type patchAreaR (patchArea, Repeated);
QuadratureRule fakeQuadratureRule;
Real refElemArea (0); //area of reference element
//compute the area of reference element
for (UInt iq = 0; iq < this->M_FESpace->qr().nbQuadPt(); iq++)
{
refElemArea += this->M_FESpace->qr().weight (iq);
}
Real wQuad (refElemArea / this->M_FESpace->refFE().nbDof() );
//Setting the quadrature Points = DOFs of the element and weight = 1
std::vector<GeoVector> coords = this->M_FESpace->refFE().refCoor();
std::vector<Real> weights (this->M_FESpace->fe().nbFEDof(), wQuad);
fakeQuadratureRule.setDimensionShape ( shapeDimension (this->M_FESpace->refFE().shape() ), this->M_FESpace->refFE().shape() );
fakeQuadratureRule.setPoints (coords, weights);
//Set the new quadrature rule
this->M_FESpace->setQuadRule (fakeQuadratureRule);
UInt totalDof = this->M_FESpace->dof().numTotalDof();
VectorElemental dk_loc (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
//Vectors for the deformation tensor
std::vector<matrix_Type> vectorDeformationF (this->M_FESpace->fe().nbFEDof(), * (this->M_deformationF) );
//Copying the displacement field into a vector with repeated map for parallel computations
solutionVect_Type dRep (* (this->M_displacement), Repeated);
VectorElemental elVecTens (this->M_FESpace->fe().nbFEDof(), this->M_FESpace->fieldDim() );
chrono.start();
//Loop on each volume
for ( UInt i = 0; i < this->M_FESpace->mesh()->numVolumes(); ++i )
{
this->M_FESpace->fe().updateFirstDerivQuadPt ( this->M_FESpace->mesh()->volumeList ( i ) );
elVecTens.zero();
this->M_marker = this->M_FESpace->mesh()->volumeList ( i ).markerID();
UInt eleID = this->M_FESpace->fe().currentLocalId();
//Extracting the local displacement
for ( UInt iNode = 0; iNode < ( UInt ) this->M_FESpace->fe().nbFEDof(); iNode++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( iNode );
for ( UInt iComp = 0; iComp < this->M_FESpace->fieldDim(); ++iComp )
{
UInt ig = this->M_FESpace->dof().localToGlobalMap ( eleID, iloc ) + iComp * this->M_FESpace->dim() + this->M_offset;
dk_loc[iloc + iComp * this->M_FESpace->fe().nbFEDof()] = dRep[ig];
}
}
//Compute the element tensor F
AssemblyElementalStructure::computeLocalDeformationGradientWithoutIdentity ( dk_loc, vectorDeformationF, this->M_FESpace->fe() );
//Compute the local vector of the principal stresses
for ( UInt nDOF = 0; nDOF < ( UInt ) this->M_FESpace->fe().nbFEDof(); nDOF++ )
{
UInt iloc = this->M_FESpace->fe().patternFirst ( nDOF );
vector_Type localDisplacement (this->M_FESpace->fieldDim(), 0.0);
for ( UInt coor = 0; coor < this->M_FESpace->fieldDim(); coor++ )
{
localDisplacement[coor] = iloc + coor * this->M_FESpace->fe().nbFEDof();
}
this->M_sigma->Scale (0.0);
this->M_firstPiola->Scale (0.0);
this->M_cofactorF->Scale (0.0);
M_deformationCylindricalF->Scale (0.0);
moveToCylindricalCoordinates (vectorDeformationF[nDOF], iloc, *M_deformationCylindricalF);
//Compute the rightCauchyC tensor
AssemblyElementalStructure::computeInvariantsRightCauchyGreenTensor (this->M_invariants, *M_deformationCylindricalF, * (this->M_cofactorF) );
//Compute the first Piola-Kirchhoff tensor
this->M_material->computeLocalFirstPiolaKirchhoffTensor (* (this->M_firstPiola), *M_deformationCylindricalF, * (this->M_cofactorF), this->M_invariants, this->M_marker);
//Compute the Cauchy tensor
AssemblyElementalStructure::computeCauchyStressTensor (* (this->M_sigma), * (this->M_firstPiola), this->M_invariants[3], *M_deformationCylindricalF);
//Compute the eigenvalue
AssemblyElementalStructure::computeEigenvalues (* (this->M_sigma), this->M_eigenvaluesR, this->M_eigenvaluesI);
//The Cauchy tensor is symmetric and therefore, the eigenvalues are real
//Check on the imaginary part of eigen values given by the Lapack method
Real sum (0);
for ( int i = 0; i < this->M_eigenvaluesI.size(); i++ )
{
sum += std::abs (this->M_eigenvaluesI[i]);
}
ASSERT_PRE ( sum < 1e-6 , "The eigenvalues of the Cauchy stress tensors have to be real!" );
std::sort ( this->M_eigenvaluesR.begin(), this->M_eigenvaluesR.end() );
//Assembling the local vector
for ( int coor = 0; coor < this->M_eigenvaluesR.size(); coor++ )
{
elVecTens[iloc + coor * this->M_FESpace->fe().nbFEDof()] = this->M_eigenvaluesR[coor];
}
}
super::reconstructElementaryVector ( elVecTens, patchAreaR, *this->M_FESpace );
//Assembling the local into global vector
for ( UInt ic = 0; ic < this->M_FESpace->fieldDim(); ++ic )
{
assembleVector (* (this->M_globalEigenvalues), elVecTens, this->M_FESpace->fe(), this->M_FESpace->dof(), ic, this->M_offset + ic * totalDof );
}
}
this->M_globalEigenvalues->globalAssemble();
chrono.stop();
this->M_displayer->leaderPrint ("Analysis done in: ", chrono.diff() );
}