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Bertbk committed Feb 29, 2024
1 parent 3e19ea3 commit 992e669
Showing 1 changed file with 66 additions and 60 deletions.
Original file line number Diff line number Diff line change
Expand Up @@ -648,28 +648,31 @@ class Qk_Hexahedron_Lagrange_GaussLobatto final : public FiniteElementBase
FUNC && func );

/**
* @brief computes the matrix B for a rotated quasi-stiffness (e.g. for pseudo-acoustic tti), defined as J^{-T}R^T A_xy R J^{-1}/det(J), where J is the Jacobian matrix, A_xy is a zero matrix except on A_xy(1,1) = 1 and A_xy(2,2) = 1 and R a rotation matrix.
* @param qa The 1d quadrature point index in xi0 direction (0,1)
* @param qb The 1d quadrature point index in xi1 direction (0,1)
* @param qc The 1d quadrature point index in xi2 direction (0,1)
* @param theta Tilt angle
* @param phi Azimuth of the tilt
* @param X Array containing the coordinates of the support points.
* @param J Array to store the Jacobian
* @param B Array to store the matrix B, in Voigt notation
*/
* @brief computes the matrix B for a rotated quasi-stiffness (e.g. for pseudo-acoustic tti), defined as J^{-T}R^T A_xy R J^{-1}/det(J),
*where J is the Jacobian matrix, A_xy is a zero matrix except on A_xy(1,1) = 1 and A_xy(2,2) = 1 and R a rotation matrix.
* @param qa The 1d quadrature point index in xi0 direction (0,1)
* @param qb The 1d quadrature point index in xi1 direction (0,1)
* @param qc The 1d quadrature point index in xi2 direction (0,1)
* @param theta Tilt angle
* @param phi Azimuth of the tilt
* @param X Array containing the coordinates of the support points.
* @param J Array to store the Jacobian
* @param B Array to store the matrix B, in Voigt notation
*/
GEOS_HOST_DEVICE
static void computeRotatedBxyMatrix( int const qa,
int const qb,
int const qc,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
real64 ( &J )[3][3],
real64 ( &B )[6] );
int const qb,
int const qc,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
real64 ( &J )[3][3],
real64 ( &B )[6] );

/**
* @brief computes the non-zero contributions of the d.o.f. indexed by q to the rotated partial-stiffness matrix R, i.e., the superposition matrix of first derivatives in x and y of the shape functions. Warning, the matrix B is obtained by computeRotatedBxyMatrix instead of usual one.
* @brief computes the non-zero contributions of the d.o.f. indexed by q to the rotated partial-stiffness matrix R, i.e., the
*superposition matrix of first derivatives in x and y of the shape functions. Warning, the matrix B is obtained by
*computeRotatedBxyMatrix instead of usual one.
* @param q The quadrature point index
* @param theta Tilt angle
* @param phi Azimuth of the tilt
Expand All @@ -679,20 +682,21 @@ class Qk_Hexahedron_Lagrange_GaussLobatto final : public FiniteElementBase
template< typename FUNC >
GEOS_HOST_DEVICE
static void computeRotatedStiffnessxyTerm( localIndex const q,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func );
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func );

/**
* @brief computes the matrix B in the case of rotated quasi-stiffness (e.g. for pseudo-acoustic tti), defined as J^{-T}R^T A_z R J^{-1}/det(J), where J is the Jacobian matrix, A_z is a zero matrix except on A_z(3,3) = 1 and R is the rotation matrix.
* @brief computes the matrix B in the case of rotated quasi-stiffness (e.g. for pseudo-acoustic tti), defined as J^{-T}R^T A_z R
*J^{-1}/det(J), where J is the Jacobian matrix, A_z is a zero matrix except on A_z(3,3) = 1 and R is the rotation matrix.
* @param qa The 1d quadrature point index in xi0 direction (0,1)
* @param qb The 1d quadrature point index in xi1 direction (0,1)
* @param qc The 1d quadrature point index in xi2 direction (0,1)
* @param theta Tilt angle
* @param theta Tilt angle
* @param phi Azimuth of the tilt
* @param X Array containing the coordinates of the support points.
* @param J Array to store the Jacobian
* @param J Array to store the Jacobian
* @param B Array to store the matrix B, in Voigt notation
*/
GEOS_HOST_DEVICE
Expand All @@ -706,7 +710,9 @@ class Qk_Hexahedron_Lagrange_GaussLobatto final : public FiniteElementBase
real64 ( &B )[6] );

/**
* @brief computes the non-zero contributions of the d.o.f. indexed by q to the rotated partial-stiffness matrix R, i.e., the superposition matrix of first derivatives in z only of the shape functions. Warning, the matrix B is obtained by computeRotatedBzMatrix instead of usual one.
* @brief computes the non-zero contributions of the d.o.f. indexed by q to the rotated partial-stiffness matrix R, i.e., the
*superposition matrix of first derivatives in z only of the shape functions. Warning, the matrix B is obtained by computeRotatedBzMatrix
*instead of usual one.
* @param q The quadrature point index
* @param theta Tilt angle
* @param phi Azimuth of the tilt
Expand All @@ -717,22 +723,22 @@ class Qk_Hexahedron_Lagrange_GaussLobatto final : public FiniteElementBase
GEOS_HOST_DEVICE
static void
computeRotatedStiffnesszTerm( localIndex const q,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func );
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func );

/**
/**
* @brief computes the transport of the rotation matrix for the tilt and azimuth angle respectively theta and phi.
* @param Rt Array of the transpose of the rotation matrix
* @param theta Tilt angle
* @param phi Azimuth of the tilt
*/
GEOS_HOST_DEVICE
static void
computeTransposeRotationMatrix(real64 (&Rt)[3][3],
real64 const theta,
real64 const phi);
computeTransposeRotationMatrix( real64 ( &Rt )[3][3],
real64 const theta,
real64 const phi );

/**
* @brief Computes the "Grad(Phi)*B*Grad(Phi)" coefficient of the stiffness term. The matrix B must be provided and Phi denotes a basis
Expand Down Expand Up @@ -1181,20 +1187,20 @@ GEOS_HOST_DEVICE
GEOS_FORCE_INLINE
void
Qk_Hexahedron_Lagrange_GaussLobatto< GL_BASIS >::

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computeTransposeRotationMatrix(real64 (&Rt)[3][3],
real64 const theta,
real64 const phi
)
computeTransposeRotationMatrix( real64 (& Rt)[3][3],
real64 const theta,
real64 const phi
)
{
Rt[0][0] = cos(phi)*cos(theta);
Rt[1][0] = sin(phi)*cos(theta);
Rt[2][0] = -sin(theta);
Rt[0][1] = -sin(phi);
Rt[1][1] = cos(phi);
Rt[0][0] = cos( phi )*cos( theta );
Rt[1][0] = sin( phi )*cos( theta );
Rt[2][0] = -sin( theta );
Rt[0][1] = -sin( phi );
Rt[1][1] = cos( phi );
Rt[2][1] = 0;
Rt[0][2] = cos(phi)*sin(theta);
Rt[1][2] = sin(phi)*sin(theta);
Rt[2][2] = cos(theta);
Rt[0][2] = cos( phi )*sin( theta );
Rt[1][2] = sin( phi )*sin( theta );
Rt[2][2] = cos( theta );

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}

template< typename GL_BASIS >
Expand Down Expand Up @@ -1300,10 +1306,10 @@ computeRotatedBzMatrix( int const qa,
real64 Az[6] = {0};
Az[2] = detJ;

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real64 Rt[3][3];
computeTransposeRotationMatrix(Rt, theta, phi);
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( S, Rt, Az); // S = R^T.Axy.R
computeTransposeRotationMatrix( Rt, theta, phi );
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( S, Rt, Az ); // S = R^T.Axy.R

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// B=det(J)*J^{-1}*R^T*Az*R*J^{-T}, using Voigt notation for B
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( B, Jinv, S);
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( B, Jinv, S );

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}

template< typename GL_BASIS >
Expand All @@ -1329,10 +1335,10 @@ computeRotatedBxyMatrix( int const qa,
Axy[0] = detJ;
Axy[1] = detJ;

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real64 Rt[3][3];
computeTransposeRotationMatrix(Rt, theta, phi);
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( S, Rt, Axy); // S = R^T.Axy.R
computeTransposeRotationMatrix( Rt, theta, phi );
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( S, Rt, Axy ); // S = R^T.Axy.R

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// B=det(J)*J^{-1}*R^T*Axy*R*J^{-T}, using Voigt notation for B
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( B, Jinv, S);
LvArray::tensorOps::Rij_eq_AikSymBklAjl< 3 >( B, Jinv, S );

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}

template< typename GL_BASIS >
Expand Down Expand Up @@ -1428,10 +1434,10 @@ GEOS_FORCE_INLINE
void
Qk_Hexahedron_Lagrange_GaussLobatto< GL_BASIS >::

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computeRotatedStiffnessxyTerm( localIndex const q,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func )
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func )
{
real64 B[6] = {0};
real64 J[3][3] = {{0}};

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Expand All @@ -1448,10 +1454,10 @@ GEOS_FORCE_INLINE
void
Qk_Hexahedron_Lagrange_GaussLobatto< GL_BASIS >::

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computeRotatedStiffnesszTerm( localIndex const q,
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func )
real64 const theta,
real64 const phi,
real64 const (&X)[8][3],
FUNC && func )
{
real64 B[6] = {0};
real64 J[3][3] = {{0}};

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Expand Down

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