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Reference documentation for deal.II version 9.6.0
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Local integrators related to elasticity problems. More...
Functions | |
template<int dim> | |
void | cell_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.) |
template<int dim, typename number > | |
void | cell_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const ArrayView< const std::vector< Tensor< 1, dim > > > &input, double factor=1.) |
template<int dim> | |
void | nitsche_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double penalty, double factor=1.) |
template<int dim> | |
void | nitsche_tangential_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double penalty, double factor=1.) |
template<int dim, typename number > | |
void | nitsche_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const ArrayView< const std::vector< double > > &input, const ArrayView< const std::vector< Tensor< 1, dim > > > &Dinput, const ArrayView< const std::vector< double > > &data, double penalty, double factor=1.) |
template<int dim, typename number > | |
void | nitsche_tangential_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const ArrayView< const std::vector< double > > &input, const ArrayView< const std::vector< Tensor< 1, dim > > > &Dinput, const ArrayView< const std::vector< double > > &data, double penalty, double factor=1.) |
template<int dim, typename number > | |
void | nitsche_residual_homogeneous (Vector< number > &result, const FEValuesBase< dim > &fe, const ArrayView< const std::vector< double > > &input, const ArrayView< const std::vector< Tensor< 1, dim > > > &Dinput, double penalty, double factor=1.) |
template<int dim> | |
void | ip_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double pen, const double int_factor=1., const double ext_factor=-1.) |
template<int dim, typename number > | |
void | ip_residual (Vector< number > &result1, Vector< number > &result2, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const ArrayView< const std::vector< double > > &input1, const ArrayView< const std::vector< Tensor< 1, dim > > > &Dinput1, const ArrayView< const std::vector< double > > &input2, const ArrayView< const std::vector< Tensor< 1, dim > > > &Dinput2, double pen, double int_factor=1., double ext_factor=-1.) |
Local integrators related to elasticity problems.
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The linear elasticity operator in weak form, namely double contraction of symmetric gradients.
\[ \int_Z \varepsilon(u): \varepsilon(v)\,dx \]
Definition at line 50 of file elasticity.h.
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Vector-valued residual operator for linear elasticity in weak form
\[ - \int_Z \varepsilon(u): \varepsilon(v) \,dx \]
Definition at line 83 of file elasticity.h.
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The matrix for the weak boundary condition of Nitsche type for linear elasticity:
\[ \int_F \Bigl(\gamma u \cdot v - n^T \epsilon(u) v - u \epsilon(v) n\Bigr)\;ds. \]
Definition at line 122 of file elasticity.h.
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The matrix for the weak boundary condition of Nitsche type for the tangential displacement in linear elasticity:
\[ \int_F \Bigl(\gamma u_\tau \cdot v_\tau - n^T \epsilon(u_\tau) v_\tau - u_\tau^T \epsilon(v_\tau) n\Bigr)\;ds. \]
Definition at line 177 of file elasticity.h.
void LocalIntegrators::Elasticity::nitsche_residual | ( | Vector< number > & | result, |
const FEValuesBase< dim > & | fe, | ||
const ArrayView< const std::vector< double > > & | input, | ||
const ArrayView< const std::vector< Tensor< 1, dim > > > & | Dinput, | ||
const ArrayView< const std::vector< double > > & | data, | ||
double | penalty, | ||
double | factor = 1. ) |
Weak boundary condition for the elasticity operator by Nitsche, namely on the face F the vector
\[ \int_F \Bigl(\gamma (u-g) \cdot v - n^T \epsilon(u) v - (u-g) \epsilon(v) n^T\Bigr)\;ds. \]
Here, u is the finite element function whose values and gradient are given in the arguments input
and Dinput
, respectively. g is the inhomogeneous boundary value in the argument data
. \(n\) is the outer normal vector and \(\gamma\) is the usual penalty parameter.
Definition at line 256 of file elasticity.h.
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The weak boundary condition of Nitsche type for the tangential displacement in linear elasticity:
\[ \int_F \Bigl(\gamma (u_\tau-g_\tau) \cdot v_\tau - n^T \epsilon(u_\tau) v - (u_\tau-g_\tau) \epsilon(v_\tau) n\Bigr)\;ds. \]
Definition at line 308 of file elasticity.h.
void LocalIntegrators::Elasticity::nitsche_residual_homogeneous | ( | Vector< number > & | result, |
const FEValuesBase< dim > & | fe, | ||
const ArrayView< const std::vector< double > > & | input, | ||
const ArrayView< const std::vector< Tensor< 1, dim > > > & | Dinput, | ||
double | penalty, | ||
double | factor = 1. ) |
Homogeneous weak boundary condition for the elasticity operator by Nitsche, namely on the face F the vector
\[ \int_F \Bigl(\gamma u \cdot v - n^T \epsilon(u) v - u \epsilon(v) n^T\Bigr)\;ds. \]
Here, u is the finite element function whose values and gradient are given in the arguments input
and Dinput
, respectively. \(n\) is the outer normal vector and \(\gamma\) is the usual penalty parameter.
Definition at line 386 of file elasticity.h.
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The interior penalty flux for symmetric gradients.
Definition at line 431 of file elasticity.h.
void LocalIntegrators::Elasticity::ip_residual | ( | Vector< number > & | result1, |
Vector< number > & | result2, | ||
const FEValuesBase< dim > & | fe1, | ||
const FEValuesBase< dim > & | fe2, | ||
const ArrayView< const std::vector< double > > & | input1, | ||
const ArrayView< const std::vector< Tensor< 1, dim > > > & | Dinput1, | ||
const ArrayView< const std::vector< double > > & | input2, | ||
const ArrayView< const std::vector< Tensor< 1, dim > > > & | Dinput2, | ||
double | pen, | ||
double | int_factor = 1., | ||
double | ext_factor = -1. ) |
Elasticity residual term for the symmetric interior penalty method.
Definition at line 539 of file elasticity.h.