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biharmonic element class More...
#include <biharmonic_elements.h>
Inheritance diagram for oomph::BiharmonicElement< DIM >:Public Member Functions | |
| double | u (const unsigned &n, const unsigned &k) const |
| access function for value, kth dof of node n More... | |
| BiharmonicElement () | |
| ~BiharmonicElement () | |
| unsigned | required_nvalue (const unsigned &n) const |
| void | output (std::ostream &outfile) |
| Output. More... | |
| void | output (std::ostream &outfile, const unsigned &n_plot) |
| output wrapper More... | |
| void | output (FILE *file_pt) |
| C-style output. More... | |
| void | output (FILE *file_pt, const unsigned &n_plot) |
| C_style output at n_plot points. More... | |
| void | output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) |
| analytic solution wrapper More... | |
| void | output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) |
| Final override. More... | |
| void | compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm) |
| computes error More... | |
| void | compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm) |
| Call the equations-class overloaded unsteady error calculation. More... | |
| Public Member Functions inherited from oomph::QHermiteElement< DIM > | |
| QHermiteElement () | |
| Constructor. More... | |
| QHermiteElement (const QHermiteElement &dummy)=delete | |
| Broken copy constructor. More... | |
| void | operator= (const QHermiteElement &)=delete |
| Broken assignment operator. More... | |
| bool | local_coord_is_valid (const Vector< double > &s) |
| Check whether the local coordinate are valid or not. More... | |
| void | move_local_coord_back_into_element (Vector< double > &s) const |
| void | shape (const Vector< double > &s, Shape &psi) const |
| void | dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const |
| void | d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const |
| double | invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| void | transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| double | s_min () const |
| Min. value of local coordinate. More... | |
| double | s_max () const |
| Max. value of local coordinate. More... | |
| void | local_coordinate_of_node (const unsigned &j, Vector< double > &s) const |
| Get local coordinates of node j in the element; vector sets its own size. More... | |
| void | local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction) |
| Get local fraction of node j in the element; vector sets its own size. More... | |
| double | local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i) |
| unsigned | nnode_1d () const |
| Return number of nodes along each element edge. More... | |
| void | output (std::ostream &outfile) |
| Output. More... | |
| void | output (std::ostream &outfile, const unsigned &n_plot) |
| Output at n_plot points. More... | |
| void | output (FILE *file_pt) |
| C-style output. More... | |
| void | output (FILE *file_pt, const unsigned &n_plot) |
| C_style output at n_plot points. More... | |
| void | get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &use_equally_spaced_interior_sample_points=false) const |
| std::string | tecplot_zone_string (const unsigned &nplot) const |
| unsigned | nplot_points (const unsigned &nplot) const |
| void | build_face_element (const int &face_index, FaceElement *face_element_pt) |
| void | shape (const Vector< double > &s, Shape &psi) const |
| Shape function for specific QHermiteElement<1> More... | |
| void | dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const |
| Derivatives of shape functions for specific QHermiteElement<1> More... | |
| void | d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const |
| void | output (std::ostream &outfile) |
| The output function for general 1D QHermiteElements. More... | |
| void | output (std::ostream &outfile, const unsigned &n_plot) |
| The output function for n_plot points in each coordinate direction. More... | |
| void | output (FILE *file_pt) |
| The C-style output function for general 1D QHermiteElements. More... | |
| void | output (FILE *file_pt, const unsigned &n_plot) |
| The C-style output function for n_plot points in each coordinate direction. More... | |
| void | build_face_element (const int &face_index, FaceElement *face_element_pt) |
| void | shape (const Vector< double > &s, Shape &psi) const |
| Shape function for specific QHermiteElement<2> More... | |
| void | dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const |
| Derivatives of shape functions for specific QHermiteElement<2> More... | |
| void | d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const |
| void | output (std::ostream &outfile) |
| The output function for QHermiteElement<2,ORDER> More... | |
| void | output (std::ostream &outfile, const unsigned &n_plot) |
| The output function for n_plot points in each coordinate direction. More... | |
| void | output (FILE *file_pt) |
| The C-style output function for QHermiteElement<2,ORDER> More... | |
| void | output (FILE *file_pt, const unsigned &n_plot) |
| The C-style output function for n_plot points in each coordinate direction. More... | |
| void | build_face_element (const int &face_index, FaceElement *face_element_pt) |
| void | get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &use_equally_spaced_interior_sample_points) const |
| std::string | tecplot_zone_string (const unsigned &nplot) const |
| unsigned | nplot_points (const unsigned &nplot) const |
| void | get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &use_equally_spaced_interior_sample_points) const |
| std::string | tecplot_zone_string (const unsigned &nplot) const |
| unsigned | nplot_points (const unsigned &nplot) const |
| Public Member Functions inherited from oomph::QHermiteElementBase | |
| QHermiteElementBase () | |
| Empty default constructor. More... | |
| QHermiteElementBase (const QHermiteElementBase &)=delete | |
| Broken copy constructor. More... | |
| void | operator= (const QHermiteElementBase &)=delete |
| Broken assignment operator. More... | |
| Public Member Functions inherited from oomph::QElementGeometricBase | |
| QElementGeometricBase () | |
| Empty default constructor. More... | |
| QElementGeometricBase (const QElementGeometricBase &)=delete | |
| Broken copy constructor. More... | |
| Public Member Functions inherited from oomph::FiniteElement | |
| void | set_dimension (const unsigned &dim) |
| void | set_nodal_dimension (const unsigned &nodal_dim) |
| void | set_nnodal_position_type (const unsigned &nposition_type) |
| Set the number of types required to interpolate the coordinate. More... | |
| void | set_n_node (const unsigned &n) |
| int | nodal_local_eqn (const unsigned &n, const unsigned &i) const |
| double | dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const |
| FiniteElement () | |
| Constructor. More... | |
| virtual | ~FiniteElement () |
| FiniteElement (const FiniteElement &)=delete | |
| Broken copy constructor. More... | |
| void | get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const |
| virtual void | set_macro_elem_pt (MacroElement *macro_elem_pt) |
| MacroElement * | macro_elem_pt () |
| Access function to pointer to macro element. More... | |
| void | get_x (const Vector< double > &s, Vector< double > &x) const |
| void | get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) |
| virtual void | get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const |
| virtual void | get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x) |
| virtual void | set_integration_scheme (Integral *const &integral_pt) |
| Set the spatial integration scheme. More... | |
| Integral *const & | integral_pt () const |
| Return the pointer to the integration scheme (const version) More... | |
| virtual void | shape_at_knot (const unsigned &ipt, Shape &psi) const |
| virtual void | dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const |
| virtual void | d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const |
| virtual double | J_eulerian (const Vector< double > &s) const |
| virtual double | J_eulerian_at_knot (const unsigned &ipt) const |
| void | check_J_eulerian_at_knots (bool &passed) const |
| void | check_jacobian (const double &jacobian) const |
| double | dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const |
| virtual double | dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const |
| virtual double | dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const |
| double | d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const |
| virtual double | d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const |
| virtual void | assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt) |
| virtual void | describe_local_dofs (std::ostream &out, const std::string ¤t_string) const |
| virtual void | describe_nodal_local_dofs (std::ostream &out, const std::string ¤t_string) const |
| virtual void | assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt) |
| Node *& | node_pt (const unsigned &n) |
| Return a pointer to the local node n. More... | |
| Node *const & | node_pt (const unsigned &n) const |
| Return a pointer to the local node n (const version) More... | |
| unsigned | nnode () const |
| Return the number of nodes. More... | |
| double | raw_nodal_position (const unsigned &n, const unsigned &i) const |
| double | raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const |
| double | raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const |
| double | raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const |
| double | raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | nodal_position (const unsigned &n, const unsigned &i) const |
| double | nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const |
| double | dnodal_position_dt (const unsigned &n, const unsigned &i) const |
| Return the i-th component of nodal velocity: dx/dt at local node n. More... | |
| double | dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const |
| double | nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const |
| double | dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const |
| virtual void | get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates) |
| virtual void | disable_ALE () |
| virtual void | enable_ALE () |
| unsigned | nnodal_position_type () const |
| bool | has_hanging_nodes () const |
| unsigned | nodal_dimension () const |
| Return the required Eulerian dimension of the nodes in this element. More... | |
| virtual unsigned | nvertex_node () const |
| virtual Node * | vertex_node_pt (const unsigned &j) const |
| virtual Node * | construct_node (const unsigned &n) |
| virtual Node * | construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt) |
| virtual Node * | construct_boundary_node (const unsigned &n) |
| virtual Node * | construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt) |
| int | get_node_number (Node *const &node_pt) const |
| virtual Node * | get_node_at_local_coordinate (const Vector< double > &s) const |
| double | raw_nodal_value (const unsigned &n, const unsigned &i) const |
| double | raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const |
| double | nodal_value (const unsigned &n, const unsigned &i) const |
| double | nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const |
| unsigned | dim () const |
| virtual ElementGeometry::ElementGeometry | element_geometry () const |
| Return the geometry type of the element (either Q or T usually). More... | |
| virtual double | interpolated_x (const Vector< double > &s, const unsigned &i) const |
| Return FE interpolated coordinate x[i] at local coordinate s. More... | |
| virtual double | interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const |
| virtual void | interpolated_x (const Vector< double > &s, Vector< double > &x) const |
| Return FE interpolated position x[] at local coordinate s as Vector. More... | |
| virtual void | interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const |
| virtual double | interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t) |
| virtual void | interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt) |
| unsigned | ngeom_data () const |
| Data * | geom_data_pt (const unsigned &j) |
| void | position (const Vector< double > &zeta, Vector< double > &r) const |
| void | position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const |
| void | dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt) |
| virtual double | zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const |
| void | interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const |
| void | locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false) |
| virtual void | node_update () |
| virtual void | identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data) |
| virtual void | identify_geometric_data (std::set< Data * > &geometric_data_pt) |
| double | size () const |
| virtual double | compute_physical_size () const |
| virtual void | point_output_data (const Vector< double > &s, Vector< double > &data) |
| void | point_output (std::ostream &outfile, const Vector< double > &s) |
| virtual unsigned | nplot_points_paraview (const unsigned &nplot) const |
| virtual unsigned | nsub_elements_paraview (const unsigned &nplot) const |
| void | output_paraview (std::ofstream &file_out, const unsigned &nplot) const |
| virtual void | write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const |
| virtual void | write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const |
| virtual void | write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const |
| virtual unsigned | nscalar_paraview () const |
| virtual void | scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const |
| virtual void | scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const |
| virtual void | scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const |
| virtual std::string | scalar_name_paraview (const unsigned &i) const |
| virtual void | output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const |
| virtual void | output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const |
| Output a time-dependent exact solution over the element. More... | |
| virtual void | write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const |
| virtual void | write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const |
| virtual void | compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm) |
| Calculate the norm of the error and that of the exact solution. More... | |
| virtual void | compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm) |
| Calculate the norm of the error and that of the exact solution. More... | |
| virtual void | compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm) |
| virtual void | compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm) |
| virtual void | compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm) |
| virtual void | compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm) |
| virtual void | compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error) |
| void | integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral) |
| Integrate Vector-valued function over element. More... | |
| void | integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral) |
| Integrate Vector-valued time-dep function over element. More... | |
| virtual unsigned | get_bulk_node_number (const int &face_index, const unsigned &i) const |
| virtual int | face_outer_unit_normal_sign (const int &face_index) const |
| Get the sign of the outer unit normal on the face given by face_index. More... | |
| virtual unsigned | nnode_on_face () const |
| void | face_node_number_error_check (const unsigned &i) const |
| Range check for face node numbers. More... | |
| virtual CoordinateMappingFctPt | face_to_bulk_coordinate_fct_pt (const int &face_index) const |
| virtual BulkCoordinateDerivativesFctPt | bulk_coordinate_derivatives_fct_pt (const int &face_index) const |
| Public Member Functions inherited from oomph::GeneralisedElement | |
| GeneralisedElement () | |
| Constructor: Initialise all pointers and all values to zero. More... | |
| virtual | ~GeneralisedElement () |
| Virtual destructor to clean up any memory allocated by the object. More... | |
| GeneralisedElement (const GeneralisedElement &)=delete | |
| Broken copy constructor. More... | |
| void | operator= (const GeneralisedElement &)=delete |
| Broken assignment operator. More... | |
| Data *& | internal_data_pt (const unsigned &i) |
| Return a pointer to i-th internal data object. More... | |
| Data *const & | internal_data_pt (const unsigned &i) const |
| Return a pointer to i-th internal data object (const version) More... | |
| Data *& | external_data_pt (const unsigned &i) |
| Return a pointer to i-th external data object. More... | |
| Data *const & | external_data_pt (const unsigned &i) const |
| Return a pointer to i-th external data object (const version) More... | |
| unsigned long | eqn_number (const unsigned &ieqn_local) const |
| int | local_eqn_number (const unsigned long &ieqn_global) const |
| unsigned | add_external_data (Data *const &data_pt, const bool &fd=true) |
| bool | external_data_fd (const unsigned &i) const |
| void | exclude_external_data_fd (const unsigned &i) |
| void | include_external_data_fd (const unsigned &i) |
| void | flush_external_data () |
| Flush all external data. More... | |
| void | flush_external_data (Data *const &data_pt) |
| Flush the object addressed by data_pt from the external data array. More... | |
| unsigned | ninternal_data () const |
| Return the number of internal data objects. More... | |
| unsigned | nexternal_data () const |
| Return the number of external data objects. More... | |
| unsigned | ndof () const |
| Return the number of equations/dofs in the element. More... | |
| void | dof_vector (const unsigned &t, Vector< double > &dof) |
| Return the vector of dof values at time level t. More... | |
| void | dof_pt_vector (Vector< double * > &dof_pt) |
| Return the vector of pointers to dof values. More... | |
| void | set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data) |
| void | assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt) |
| void | describe_dofs (std::ostream &out, const std::string ¤t_string) const |
| void | add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt) |
| virtual void | assign_local_eqn_numbers (const bool &store_local_dof_pt) |
| virtual void | complete_setup_of_dependencies () |
| virtual void | get_residuals (Vector< double > &residuals) |
| virtual void | get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian) |
| virtual void | get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix) |
| virtual void | get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix) |
| virtual void | get_dresiduals_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam) |
| virtual void | get_djacobian_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam) |
| virtual void | get_djacobian_and_dmass_matrix_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam) |
| virtual void | get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product) |
| virtual void | get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product) |
| virtual void | get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector) |
| virtual void | compute_norm (Vector< double > &norm) |
| virtual void | compute_norm (double &norm) |
| Public Member Functions inherited from oomph::GeomObject | |
| GeomObject () | |
| Default constructor. More... | |
| GeomObject (const unsigned &ndim) | |
| GeomObject (const unsigned &nlagrangian, const unsigned &ndim) | |
| GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt) | |
| GeomObject (const GeomObject &dummy)=delete | |
| Broken copy constructor. More... | |
| void | operator= (const GeomObject &)=delete |
| Broken assignment operator. More... | |
| virtual | ~GeomObject () |
| (Empty) destructor More... | |
| unsigned | nlagrangian () const |
| Access function to # of Lagrangian coordinates. More... | |
| unsigned | ndim () const |
| Access function to # of Eulerian coordinates. More... | |
| void | set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim) |
| Set # of Lagrangian and Eulerian coordinates. More... | |
| TimeStepper *& | time_stepper_pt () |
| TimeStepper * | time_stepper_pt () const |
| virtual void | position (const double &t, const Vector< double > &zeta, Vector< double > &r) const |
| virtual void | dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const |
| virtual void | d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const |
| virtual void | d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const |
| Public Member Functions inherited from oomph::BiharmonicEquations< DIM > | |
| BiharmonicEquations () | |
| Constructor (must initialise the Source_fct_pt to null) More... | |
| ~BiharmonicEquations () | |
| virtual void | get_source (const unsigned &ipt, const Vector< double > &x, double &source) const |
| gets source strength More... | |
| void | fill_in_contribution_to_residuals (Vector< double > &residuals) |
| wrapper function, adds contribution to residual More... | |
| void | fill_in_contribution_to_jacobian (Vector< double > &residual, DenseMatrix< double > &jacobian) |
| wrapper function, adds contribution to residual and generic More... | |
| void | output_fluid_velocity (std::ostream &outfile, const unsigned &nplot) |
| output fluid velocity field More... | |
| void | interpolated_dudx (const Vector< double > &s, Vector< double > &dudx) |
| output with nplot points More... | |
| double | interpolated_u_biharmonic (const Vector< double > &s) |
| calculates interpolated u at s More... | |
| unsigned | self_test () |
| self test wrapper More... | |
| unsigned | get_d2_dof () |
| return number of second derivate degrees of freedom More... | |
| unsigned | ndof_types () const |
| void | get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const |
| SourceFctPt & | source_fct_pt () |
| Access functions for the source function pointer. More... | |
| SourceFctPt | source_fct_pt () const |
| Access functions for the source function pointers (const version) More... | |
Additional Inherited Members | |
| Public Types inherited from oomph::FiniteElement | |
| typedef void(* | SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &) |
| typedef void(* | UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &) |
| Public Types inherited from oomph::BiharmonicEquations< DIM > | |
| typedef void(* | SourceFctPt) (const Vector< double > &x, double &u) |
| source function type definition More... | |
| Static Public Attributes inherited from oomph::FiniteElement | |
| static double | Tolerance_for_singular_jacobian = 1.0e-16 |
| Tolerance below which the jacobian is considered singular. More... | |
| static bool | Accept_negative_jacobian = false |
| static bool | Suppress_output_while_checking_for_inverted_elements |
| Static Public Attributes inherited from oomph::GeneralisedElement | |
| static bool | Suppress_warning_about_repeated_internal_data |
| static bool | Suppress_warning_about_repeated_external_data = true |
| static double | Default_fd_jacobian_step = 1.0e-8 |
| Protected Member Functions inherited from oomph::FiniteElement | |
| virtual void | assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const |
| virtual void | assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const |
| virtual void | assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const |
| template<unsigned DIM> | |
| double | invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| virtual double | local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| double | local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const |
| virtual double | local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| virtual void | dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| template<unsigned DIM> | |
| void | dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| virtual void | d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| template<unsigned DIM> | |
| void | d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| virtual void | transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const |
| void | transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const |
| template<unsigned DIM> | |
| void | transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| template<unsigned DIM> | |
| void | transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| virtual void | fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian) |
| void | fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian) |
| virtual void | update_before_nodal_fd () |
| virtual void | reset_after_nodal_fd () |
| virtual void | update_in_nodal_fd (const unsigned &i) |
| virtual void | reset_in_nodal_fd (const unsigned &i) |
| void | fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian) |
| template<> | |
| double | invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| Zero-d specialisation of function to calculate inverse of jacobian mapping. More... | |
| template<> | |
| double | invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| One-d specialisation of function to calculate inverse of jacobian mapping. More... | |
| template<> | |
| double | invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| Two-d specialisation of function to calculate inverse of jacobian mapping. More... | |
| template<> | |
| double | invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const |
| template<> | |
| void | dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| template<> | |
| void | dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| template<> | |
| void | dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| template<> | |
| void | dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const |
| template<> | |
| void | d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| template<> | |
| void | d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| template<> | |
| void | d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| template<> | |
| void | d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const |
| template<> | |
| void | transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| template<> | |
| void | transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| template<> | |
| void | transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| template<> | |
| void | transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const |
| Protected Member Functions inherited from oomph::GeneralisedElement | |
| unsigned | add_internal_data (Data *const &data_pt, const bool &fd=true) |
| bool | internal_data_fd (const unsigned &i) const |
| void | exclude_internal_data_fd (const unsigned &i) |
| void | include_internal_data_fd (const unsigned &i) |
| void | clear_global_eqn_numbers () |
| void | add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt) |
| virtual void | assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt) |
| virtual void | assign_additional_local_eqn_numbers () |
| int | internal_local_eqn (const unsigned &i, const unsigned &j) const |
| int | external_local_eqn (const unsigned &i, const unsigned &j) |
| void | fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false) |
| void | fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false) |
| void | fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false) |
| void | fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false) |
| virtual void | update_before_internal_fd () |
| virtual void | reset_after_internal_fd () |
| virtual void | update_in_internal_fd (const unsigned &i) |
| virtual void | reset_in_internal_fd (const unsigned &i) |
| virtual void | update_before_external_fd () |
| virtual void | reset_after_external_fd () |
| virtual void | update_in_external_fd (const unsigned &i) |
| virtual void | reset_in_external_fd (const unsigned &i) |
| virtual void | fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix) |
| virtual void | fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix) |
| virtual void | fill_in_contribution_to_dresiduals_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam) |
| virtual void | fill_in_contribution_to_djacobian_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam) |
| virtual void | fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam) |
| virtual void | fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product) |
| virtual void | fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product) |
| virtual void | fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector) |
| Protected Member Functions inherited from oomph::BiharmonicEquations< DIM > | |
| virtual void | fill_in_generic_residual_contribution_biharmonic (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned JFLAG) |
| Protected Attributes inherited from oomph::FiniteElement | |
| MacroElement * | Macro_elem_pt |
| Pointer to the element's macro element (NULL by default) More... | |
| Protected Attributes inherited from oomph::GeomObject | |
| unsigned | NLagrangian |
| Number of Lagrangian (intrinsic) coordinates. More... | |
| unsigned | Ndim |
| Number of Eulerian coordinates. More... | |
| TimeStepper * | Geom_object_time_stepper_pt |
| Protected Attributes inherited from oomph::BiharmonicEquations< DIM > | |
| SourceFctPt | Source_fct_pt |
| Pointer to source function: More... | |
| Vector< int > | Local_eqn |
| Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC) More... | |
| Static Protected Attributes inherited from oomph::FiniteElement | |
| static const unsigned | Default_Initial_Nvalue = 0 |
| Default value for the number of values at a node. More... | |
| static const double | Node_location_tolerance = 1.0e-14 |
| static const unsigned | N2deriv [] = {0, 1, 3, 6} |
| Static Protected Attributes inherited from oomph::GeneralisedElement | |
| static DenseMatrix< double > | Dummy_matrix |
| static std::deque< double * > | Dof_pt_deque |
biharmonic element class
|
inline |
|
inline |
|
inlinevirtual |
computes error
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::compute_error(), and calibrate::error.
|
inlinevirtual |
Call the equations-class overloaded unsteady error calculation.
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::compute_error(), and calibrate::error.
|
inlinevirtual |
C-style output.
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output().
|
inlinevirtual |
C_style output at n_plot points.
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output().
|
inlinevirtual |
Output.
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output().
|
inlinevirtual |
output wrapper
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output().
|
inlinevirtual |
Final override.
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output_fct().
|
inlinevirtual |
analytic solution wrapper
Reimplemented from oomph::BiharmonicEquations< DIM >.
References oomph::BiharmonicEquations< DIM >::output_fct().
|
inlinevirtual |
Required # of ‘values’ (pinned or dofs) at node n
Reimplemented from oomph::FiniteElement.
References DIM.
|
inlinevirtual |
access function for value, kth dof of node n
Implements oomph::BiharmonicEquations< DIM >.
References k, oomph::FiniteElement::node_pt(), and oomph::Node::value().
1.9.1 