#include <discontinuous_galerkin_space_time_unsteady_heat_mixed_order_elements.h>

Inheritance diagram for oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >:

Public Member Functions
	SpaceTimeUnsteadyHeatMixedOrderEquations ()

	SpaceTimeUnsteadyHeatMixedOrderEquations (const SpaceTimeUnsteadyHeatMixedOrderEquations &dummy)=delete
	Broken copy constructor. More...

void	disable_ALE ()

void	enable_ALE ()

void	compute_norm (double &norm)
	Compute norm of FE solution. More...

void	output (std::ostream &outfile)
	Output with default number of plot points. More...

void	output (std::ostream &outfile, const unsigned &nplot)

void	output (FILE *file_pt)
	C_style output with default number of plot points. More...

void	output (FILE *file_pt, const unsigned &nplot)

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

virtual void	output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error and norm against exact solution. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Get error and norm against exact solution. More...

void	output_element_paraview (std::ofstream &outfile, const unsigned &nplot)

unsigned	nscalar_paraview () const

void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const

void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const

void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

std::string	scalar_name_paraview (const unsigned &i) const

SpaceTimeUnsteadyHeatSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

SpaceTimeUnsteadyHeatSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

virtual void	get_source_ust_heat (const double &t, const unsigned &ipt, const Vector< double > &x, double &source) const

const double &	alpha () const
	Alpha parameter (thermal inertia) More...

double *&	alpha_pt ()
	Pointer to Alpha parameter (thermal inertia) More...

const double &	beta () const
	Beta parameter (thermal conductivity) More...

double *&	beta_pt ()
	Pointer to Beta parameter (thermal conductivity) More...

void	get_flux (const Vector< double > &s, Vector< double > &flux) const
	Get flux: flux[i]=du/dx_i. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Compute element residual Vector (wrapper) More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute element residual Vector and element Jacobian matrix (wrapper) More...

double	interpolated_u_ust_heat (const Vector< double > &s) const
	Return FE representation of function value u(s) at local coordinate s. More...

virtual unsigned	u_index_ust_heat () const

double	interpolated_u_ust_heat (const unsigned &t, const Vector< double > &s) const

double	du_dt_ust_heat (const unsigned &n) const

double	interpolated_du_dt_ust_heat (const Vector< double > &s) const

unsigned	self_test ()
	Self-test: Return 0 for OK. More...

virtual double	dshape_and_dtest_eulerian_ust_heat (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_ust_heat (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

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...

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

virtual void	move_local_coord_back_into_element (Vector< double > &s) const

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)

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 (const Vector< double > &s, Shape &psi) const =0

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) 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 &current_string) const

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_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...

virtual unsigned	nnode_1d () const

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 unsigned	required_nvalue (const unsigned &n) const

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)

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

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 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	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const

virtual std::string	tecplot_zone_string (const unsigned &nplot) const

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 unsigned	nplot_points (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 void	build_face_element (const int &face_index, FaceElement *face_element_pt)

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 &current_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 &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_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 unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

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

Protected Member Functions
virtual void	shape_ust_heat (const Vector< double > &s, Shape &psi) const =0
	Shape functions w.r.t. to local coords. More...

virtual void	dshape_local_ust_heat (const Vector< double > &s, Shape &psi, DShape &dpsidx) const =0
	Shape functions & derivs. w.r.t. to local coords. More...

virtual void	dtest_local_ust_heat (const Vector< double > &s, Shape &test, DShape &dtestdx) const =0
	Test functions & derivs. w.r.t. to local coords. More...

virtual void	fill_in_generic_residual_contribution_ust_heat (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

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	invert_jacobian_mapping (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

virtual void	transform_second_derivatives (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_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)

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 &parameter_pt, Vector< double > &dres_dparam)

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_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 Attributes
SpaceTimeUnsteadyHeatSourceFctPt	Source_fct_pt
	Pointer to source function: More...

bool	ALE_is_disabled

double *	Alpha_pt
	Pointer to Alpha parameter (thermal inertia) More...

double *	Beta_pt
	Pointer to Beta parameter (thermal conductivity) More...

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

Static Private Attributes
static double	Default_alpha_parameter = 1.0
	Default value for Alpha parameter (thermal inertia) More...

static double	Default_beta_parameter = 1.0
	Default value for Beta parameter (thermal conductivity) More...

Additional Inherited Members
Public Types inherited from oomph::SpaceTimeUnsteadyHeatEquationsBase
typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

typedef void(*	SpaceTimeUnsteadyHeatSourceFctPt) (const double &time, const Vector< double > &x, double &u)

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)

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

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

Detailed Description

template<unsigned SPATIAL_DIM>
class oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >

A class for all isoparametric elements that solve the SpaceTimeUnsteadyHeatMixedOrder equations.

\[ \frac{\partial^2 u}{\partial x_i^2}=\frac{\partial u}{\partial t}+f(t,x_j) \]

This contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class. Note that this class assumes an isoparametric formulation, i.e. that the scalar unknown is interpolated using the same shape funcitons as the position.

Constructor & Destructor Documentation

◆ SpaceTimeUnsteadyHeatMixedOrderEquations() [1/2]

template<unsigned SPATIAL_DIM>

oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations ( )

inline

Constructor: Initialises the Source_fct_pt to null and sets flag to use ALE formulation of the equations. Also, set Alpha (thermal inertia) and Beta (thermal conductivity) parameters to defaults (both one for natural scaling).

       : Source_fct_pt(0), ALE_is_disabled(false)
     {
       // Set Alpha parameter to default (one for natural scaling)
       Alpha_pt = &Default_alpha_parameter;
  
       // Set Beta parameter to default (one for natural scaling)
       Beta_pt = &Default_beta_parameter;
     } // End of SpaceTimeUnsteadyHeatMixedOrderEquations

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Alpha_pt, oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Beta_pt, oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Default_alpha_parameter, and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Default_beta_parameter.

◆ SpaceTimeUnsteadyHeatMixedOrderEquations() [2/2]

template<unsigned SPATIAL_DIM>

oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations ( const SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ alpha()

template<unsigned SPATIAL_DIM>

const double& oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::alpha ( ) const

inline

Alpha parameter (thermal inertia)

     {
       // Return the value of Alpha
       return *Alpha_pt;
     } // End of alpha

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Alpha_pt.

◆ alpha_pt()

template<unsigned SPATIAL_DIM>

double*& oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::alpha_pt ( )

inline

Pointer to Alpha parameter (thermal inertia)

     {
       // Return the pointer to Alpha
       return Alpha_pt;
     } // End of alpha_pt

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Alpha_pt.

◆ beta()

template<unsigned SPATIAL_DIM>

const double& oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::beta ( ) const

inline

Beta parameter (thermal conductivity)

     {
       // Return the pointer to Beta
       return *Beta_pt;
     } // End of beta

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Beta_pt.

◆ beta_pt()

template<unsigned SPATIAL_DIM>

double*& oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::beta_pt ( )

inline

Pointer to Beta parameter (thermal conductivity)

     {
       // Return the pointer to Beta
       return Beta_pt;
     } // End of beta_pt

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Beta_pt.

◆ compute_error() [1/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		double &	error,
		double &	norm
	)

virtual

Get error and norm against exact solution.

Validate against exact solution

Solution is provided via function pointer. Plot error at a given number of plot points.

Reimplemented from oomph::FiniteElement.

   {
     // Initialise error value
     error = 0.0;
  
     // Initialise norm value
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Vector for spatial coordinates
     Vector<double> spatial_coordinates(SPATIAL_DIM, 0.0);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Tecplot header info
     outfile << "ZONE" << std::endl;
  
     // Exact solution vector (here it's simply a scalar)
     Vector<double> exact_soln(1, 0.0);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Get the i-th local coordinate at the ipt-th integration point
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       double u_fe = interpolated_u_ust_heat(s);
  
       // Loop over the spatial coordinates
       for (unsigned i = 0; i < SPATIAL_DIM; i++)
       {
         // Assign the i-th spatial coordinate
         spatial_coordinates[i] = interpolated_x(s, i);
  
         // Output the i-th coordinate at the point
         outfile << spatial_coordinates[i] << " ";
       }
  
       // Output the i-th coordinate at this point
       outfile << interpolated_x(s, SPATIAL_DIM) << " ";
  
       // Get exact solution at this point
       (*exact_soln_pt)(spatial_coordinates, exact_soln);
  
       // Output the error
       outfile << exact_soln[0] << " " << exact_soln[0] - u_fe << std::endl;
  
       // Add to (exact) solution norm value
       norm += exact_soln[0] * exact_soln[0] * W;
  
       // Update the error norm value
       error += (exact_soln[0] - u_fe) * (exact_soln[0] - u_fe) * W;
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
   } // End of compute_error

References calibrate::error, ProblemParameters::exact_soln(), i, J, s, w, and oomph::QuadTreeNames::W.

◆ compute_error() [2/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::compute_error	(	std::ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt,
		const double &	time,
		double &	error,
		double &	norm
	)

virtual

Get error and norm against exact solution.

Validate against exact solution at time t.

Solution is provided via function pointer. Plot error at a given number of plot points.

Reimplemented from oomph::FiniteElement.

   {
     // Initialise error value
     error = 0.0;
  
     // Initialise norm value
     norm = 0.0;
  
     // Storage for the time value
     double interpolated_t = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Vector for spatial coordinates
     Vector<double> spatial_coordinates(SPATIAL_DIM, 0.0);
  
     // Set the value of n_intpt
     unsigned n_int_pt = integral_pt()->nweight();
  
     // Exact solution vector (here it's simply a scalar)
     Vector<double> exact_soln(1, 0.0);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_int_pt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       double u_fe = interpolated_u_ust_heat(s);
  
       // Loop over the spatial coordinates
       for (unsigned i = 0; i < SPATIAL_DIM; i++)
       {
         // Assign the i-th spatial coordinate
         spatial_coordinates[i] = interpolated_x(s, i);
       }
  
       // Get the time value
       interpolated_t = interpolated_x(s, SPATIAL_DIM);
  
       // Get the exact solution at this point
       (*exact_soln_pt)(interpolated_t, spatial_coordinates, exact_soln);
  
       // Add to (exact) solution norm value
       norm += exact_soln[0] * exact_soln[0] * W;
  
       // Update the error norm value
       error += (exact_soln[0] - u_fe) * (exact_soln[0] - u_fe) * W;
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
  
     // The number of plot points
     unsigned n_plot = 3;
  
     // Tecplot header info
     outfile << tecplot_zone_string(n_plot);
  
     // Get the number of plot points
     unsigned num_plot_points = nplot_points(n_plot);
  
     // Loop over plot points
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, n_plot, s);
  
       // Loop over the spatial coordinates
       for (unsigned i = 0; i < SPATIAL_DIM; i++)
       {
         // Assign the i-th spatial coordinate
         spatial_coordinates[i] = interpolated_x(s, i);
  
         // Output the i-th coordinate at the point
         outfile << spatial_coordinates[i] << " ";
       }
  
       // Get the time value
       interpolated_t = interpolated_x(s, SPATIAL_DIM);
  
       // Get FE function value
       double u_fe = interpolated_u_ust_heat(s);
  
       // Output the time value at this point
       outfile << interpolated_t << " ";
  
       // Get the exact solution at this point
       (*exact_soln_pt)(interpolated_t, spatial_coordinates, exact_soln);
  
       // Output the exact solution at this point
       outfile << exact_soln[0] - u_fe << std::endl;
     } // for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, n_plot);
   } // End of compute_error

References calibrate::error, ProblemParameters::exact_soln(), i, J, s, w, and oomph::QuadTreeNames::W.

◆ compute_norm()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::compute_norm ( double & norm )

virtual

Compute norm of FE solution.

Reimplemented from oomph::GeneralisedElement.

   {
     // Initialise
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Vector for coordinates
     Vector<double> x(SPATIAL_DIM + 1, 0.0);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Get the i-th local coordinate at the ipt-th integration point
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get Jacobian of mapping
       double J = J_eulerian(s);
  
       // Pre-multiply the weights and the Jacobian
       double W = w * J;
  
       // Get FE function value
       double u = interpolated_u_ust_heat(s);
  
       // Update the norm value
       norm += u * u * W;
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
   } // End of compute_norm

References i, J, s, w, oomph::QuadTreeNames::W, and plotDoE::x.

◆ disable_ALE()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::disable_ALE ( )

inlinevirtual

Disable ALE, i.e. assert the mesh is not moving – you do this at your own risk!

Reimplemented from oomph::FiniteElement.

     {
       // Set the flag to true
       ALE_is_disabled = true;
     } // End of disable_ALE

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::ALE_is_disabled.

◆ dshape_and_dtest_eulerian_at_knot_ust_heat()

template<unsigned SPATIAL_DIM>

virtual double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dshape_and_dtest_eulerian_at_knot_ust_heat	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

pure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping

Implemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

◆ dshape_and_dtest_eulerian_ust_heat()

template<unsigned SPATIAL_DIM>

virtual double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dshape_and_dtest_eulerian_ust_heat	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

pure virtual

Shape/test functions and derivs w.r.t. to global coords at local coordinate s; return Jacobian of mapping

Implemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

◆ dshape_local_ust_heat()

template<unsigned SPATIAL_DIM>

virtual void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dshape_local_ust_heat	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx
	)		const

protectedpure virtual

Shape functions & derivs. w.r.t. to local coords.

Implemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_flux(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_du_dt_ust_heat().

◆ dtest_local_ust_heat()

template<unsigned SPATIAL_DIM>

virtual void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dtest_local_ust_heat	(	const Vector< double > &	s,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Test functions & derivs. w.r.t. to local coords.

Implemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

◆ du_dt_ust_heat()

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::du_dt_ust_heat ( const unsigned & n ) const

inline

Calculate du/dt at the n-th local node. Uses suitably interpolated value for hanging nodes.

     {
       // Storage for the local coordinates
       Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
       // Get the local coordinate at the n-th node
       local_coordinate_of_node(n, s);
  
       // Return the interpolated du/dt value
       return interpolated_du_dt_ust_heat(s);
     } // End of du_dt_ust_heat

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_du_dt_ust_heat(), oomph::FiniteElement::local_coordinate_of_node(), n, and s.

◆ enable_ALE()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::enable_ALE ( )

inlinevirtual

(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. Note: By default, ALE is enabled, at the expense of possibly creating unnecessary work in problems where the mesh is, in fact, stationary.

Reimplemented from oomph::FiniteElement.

     {
       // Set the flag to false
       ALE_is_disabled = false;
     } // End of enable_ALE

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::ALE_is_disabled.

◆ fill_in_contribution_to_jacobian()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Compute element residual Vector and element Jacobian matrix (wrapper)

Reimplemented from oomph::FiniteElement.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution_ust_heat(residuals, jacobian, 1);
     } // End of fill_in_contribution_to_jacobian

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_generic_residual_contribution_ust_heat().

◆ fill_in_contribution_to_residuals()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Compute element residual Vector (wrapper)

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic residuals function with flag set to 0
       // using a dummy matrix argument
       fill_in_generic_residual_contribution_ust_heat(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     } // End of fill_in_contribution_to_residuals

References oomph::GeneralisedElement::Dummy_matrix, and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_generic_residual_contribution_ust_heat().

◆ fill_in_generic_residual_contribution_ust_heat()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_generic_residual_contribution_ust_heat	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

protectedvirtual

Compute element residual Vector only (if flag=and/or element Jacobian matrix

Compute element residual vector and/or element Jacobian matrix

flag=0: compute only residual vector flag=1: compute both

Pure version without hanging nodes

Reimplemented in oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >.

   {
     // Find out how many nodes there are
     unsigned n_node = nnode();
  
     // Find the index at which the variable is stored
     unsigned u_nodal_index = u_index_ust_heat();
  
     // Set up memory for the shape functions
     Shape psi(n_node);
  
     // Set up memory for the test functions
     Shape test(n_node);
  
     // Allocate space for the derivatives of the shape functions
     DShape dpsidx(n_node, SPATIAL_DIM + 1);
  
     // Allocate space for the derivatives of the test functions
     DShape dtestdx(n_node, SPATIAL_DIM + 1);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Storage for the local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Get the Alpha parameter
     double alpha_local = alpha();
  
     // Get the Beta parameter
     double beta_local = beta();
  
     // Integer to hold the local equation
     int local_eqn = 0;
  
     // Integer to hold the local unknowns
     int local_unknown = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Calculate the i-th local coordinate
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape and test functions
       double J = dshape_and_dtest_eulerian_at_knot_ust_heat(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Storage for the interpolated time value
       double interpolated_t = 0.0;
  
       // Storage for the interpolated solution value
       double interpolated_u = 0.0;
  
       // Storage for the interpolated time-derivative of the solution
       double interpolated_dudt = 0.0;
  
       // Storage for the spatial coordinates
       Vector<double> interpolated_x(SPATIAL_DIM, 0.0);
  
       // Storage for the spatial derivatives of the solution
       Vector<double> interpolated_dudx(SPATIAL_DIM, 0.0);
  
       // Storage for the mesh velocity
       Vector<double> mesh_velocity(SPATIAL_DIM, 0.0);
  
       //-------------------------------------------------
       // Calculate derivatives and source function value:
       //-------------------------------------------------
       // Loop over the nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the nodal value at the l-th node
         double u_value = raw_nodal_value(l, u_nodal_index);
  
         // Update the interpolated time value
         interpolated_t += raw_nodal_position(l, SPATIAL_DIM) * psi(l);
  
         // Loop over the coordinate directions (both spatial AND time)
         for (unsigned j = 0; j < SPATIAL_DIM; j++)
         {
           // Update the interpolated x value
           interpolated_x[j] += raw_nodal_position(l, j) * psi(l);
  
           // Update the interpolated du/dx_j value
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
  
         // Update the interpolated u value
         interpolated_u += u_value * psi(l);
  
         // Update the interpolated du/dt value
         interpolated_dudt += u_value * dpsidx(l, SPATIAL_DIM);
       } // for (unsigned l=0;l<n_node;l++)
  
       // Initialise the source term value
       double source = 0.0;
  
       // Get the interpolated source term value
       get_source_ust_heat(interpolated_t, ipt, interpolated_x, source);
  
       //---------------------------------
       // Assemble residuals and Jacobian:
       //---------------------------------
       // Loop over the nodes (or equivalently the test functions)
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the local equation number
         local_eqn = nodal_local_eqn(l, u_nodal_index);
  
         // If it's not a boundary condition
         if (local_eqn >= 0)
         {
           // Add source term and time derivative
           residuals[local_eqn] +=
             (source + alpha_local * interpolated_dudt) * test(l) * W;
  
           // Loop over the coordinate directions
           for (unsigned k = 0; k < SPATIAL_DIM; k++)
           {
             // Add in the contribution from the Laplace operator
             residuals[local_eqn] +=
               beta_local * interpolated_dudx[k] * dtestdx(l, k) * W;
           }
  
           //------------------------
           // Calculate the Jacobian:
           //------------------------
           // If we also need to construct the Jacobian
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               // Get the local equation number
               local_unknown = nodal_local_eqn(l2, u_nodal_index);
  
               // If we're at a non-zero degree of freedom add in the entry
               if (local_unknown >= 0)
               {
                 // Add in the time derivative contribution
                 jacobian(local_eqn, local_unknown) +=
                   (alpha_local * test(l) * dpsidx(l2, SPATIAL_DIM) * W);
  
                 // Laplace operator
                 for (unsigned i = 0; i < SPATIAL_DIM; i++)
                 {
                   // Add the test function contribution to the Jacobian
                   jacobian(local_eqn, local_unknown) +=
                     (beta_local * dpsidx(l2, i) * dtestdx(l, i) * W);
                 }
               } // if (local_unknown>=0)
             } // for (unsigned l2=0;l2<n_node;l2++)
           } // if (flag)
         } // if (local_eqn>=0)
       } // for (unsigned l=0;l<n_node;l++)
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
   } // End of fill_in_generic_residual_contribution_ust_heat

References alpha, beta, i, J, j, k, s, TestProblem::source(), Eigen::test, w, and oomph::QuadTreeNames::W.

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_contribution_to_jacobian(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::fill_in_contribution_to_residuals().

◆ get_flux()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)		const

inline

Get flux: flux[i]=du/dx_i.

     {
       // Find out how many nodes there are in the element
       unsigned n_node = nnode();
  
       // Find the index at which the variable is stored
       unsigned u_nodal_index = u_index_ust_heat();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node);
  
       // Set up memory for the derivatives of the shape functions
       DShape dpsidx(n_node, SPATIAL_DIM + 1);
  
       //------------dshape_eulerian(s,psi,dpsidx)----------------------------
       // Find the element dimension
       const unsigned el_dim = this->dim();
  
       // Get the values of the shape functions and their local derivatives;
       // temporarily stored in dpsi
       dshape_local_ust_heat(s, psi, dpsidx);
  
       // Allocate memory for the inverse jacobian
       DenseMatrix<double> inverse_jacobian(el_dim);
  
       // Now calculate the inverse jacobian
       local_to_eulerian_mapping(dpsidx, inverse_jacobian);
  
       // Now set the values of the derivatives to be dpsidx
       transform_derivatives(inverse_jacobian, dpsidx);
       //------------dshape_eulerian(s,psi,dpsidx)----------------------------
  
       // Loop over the entries of the flux vector
       for (unsigned j = 0; j < SPATIAL_DIM; j++)
       {
         // Initialise j-th flux entry to zero
         flux[j] = 0.0;
       }
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over derivative directions
         for (unsigned j = 0; j < SPATIAL_DIM; j++)
         {
           // Update the flux value
           flux[j] += nodal_value(l, u_nodal_index) * dpsidx(l, j);
         }
       } // for (unsigned l=0;l<n_node;l++)
     } // End of get_flux

References oomph::FiniteElement::dim(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dshape_local_ust_heat(), el_dim, ProblemParameters::flux(), j, oomph::FiniteElement::local_to_eulerian_mapping(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::transform_derivatives(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

◆ get_source_ust_heat()

template<unsigned SPATIAL_DIM>

virtual void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_source_ust_heat	(	const double &	t,
		const unsigned &	ipt,
		const Vector< double > &	x,
		double &	source
	)		const

inlinevirtual

Get source term at continous time t and (Eulerian) position x. Virtual so it can be overloaded in derived multi-physics elements.

     {
       // If no source function has been set, return zero
       if (Source_fct_pt == 0)
       {
         // Set the source term value to zero
         source = 0.0;
       }
       // Otherwise return the appropriate value
       else
       {
         // Get source strength
         (*Source_fct_pt)(t, x, source);
       }
     } // End of get_source_ust_heat

References TestProblem::source(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Source_fct_pt, plotPSD::t, and plotDoE::x.

◆ interpolated_du_dt_ust_heat()

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_du_dt_ust_heat ( const Vector< double > & s ) const

inline

Return FE representation of function value du/dt(s) at local coordinate s

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Find the index at which the variable is stored
       unsigned u_nodal_index = u_index_ust_heat();
  
       // Local shape function
       Shape psi(n_node);
  
       // Allocate space for the derivatives of the shape functions
       DShape dpsidx(n_node, SPATIAL_DIM + 1);
  
       //------------dshape_eulerian(s,psi,dpsidx)----------------------------
       // Find the element dimension
       const unsigned el_dim = this->dim();
  
       // Get the values of the shape functions and their local derivatives;
       // temporarily stored in dpsi
       dshape_local_ust_heat(s, psi, dpsidx);
  
       // Allocate memory for the inverse jacobian
       DenseMatrix<double> inverse_jacobian(el_dim);
  
       // Now calculate the inverse jacobian
       local_to_eulerian_mapping(dpsidx, inverse_jacobian);
  
       // Now set the values of the derivatives to be dpsidx
       transform_derivatives(inverse_jacobian, dpsidx);
       //------------dshape_eulerian(s,psi,dpsidx)----------------------------
  
       // Initialise value of du/dt
       double interpolated_dudt = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the interpolated du/dt value
         interpolated_dudt +=
           nodal_value(l, u_nodal_index) * dpsidx(l, SPATIAL_DIM);
       }
  
       // Return the interpolated du/dt value
       return interpolated_dudt;
     } // End of interpolated_du_dt_ust_heat

References oomph::FiniteElement::dim(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::dshape_local_ust_heat(), el_dim, oomph::FiniteElement::local_to_eulerian_mapping(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::transform_derivatives(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::du_dt_ust_heat().

◆ interpolated_u_ust_heat() [1/2]

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_u_ust_heat	(	const unsigned &	t,
		const Vector< double > &	s
	)		const

inline

Return FE representation of function value u(s) at local coordinate s at previous time t (t=0: present) DRAIG: This needs to be broken; doesn't make sense in space-time elements!

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Find the index at which the variable is stored
       unsigned u_nodal_index = u_index_ust_heat();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape_ust_heat(s, psi);
  
       // Initialise value of u
       double interpolated_u = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the interpolated u value
         interpolated_u += nodal_value(t, l, u_nodal_index) * psi[l];
       }
  
       // Return the interpolated u value
       return interpolated_u;
     } // End of interpolated_u_ust_heat

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::shape_ust_heat(), plotPSD::t, and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

◆ interpolated_u_ust_heat() [2/2]

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_u_ust_heat ( const Vector< double > & s ) const

inline

Return FE representation of function value u(s) at local coordinate s.

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Find the index at which the variable is stored
       unsigned u_nodal_index = u_index_ust_heat();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of the shape functions at local coordinate s
       shape_ust_heat(s, psi);
  
       // Initialise value of u
       double interpolated_u = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the interpolated u value
         interpolated_u += nodal_value(l, u_nodal_index) * psi[l];
       }
  
       // Return the interpolated u value
       return interpolated_u;
     } // End of interpolated_u_ust_heat

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::shape_ust_heat(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat().

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::scalar_value_paraview().

◆ nscalar_paraview()

template<unsigned SPATIAL_DIM>

unsigned oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::nscalar_paraview ( ) const

inlinevirtual

Number of scalars/fields output by this element. Reimplements broken virtual function in base class.

Reimplemented from oomph::FiniteElement.

     {
       // Only one field to output
       return 1;
     } // End of nscalar_paraview

◆ output() [1/4]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output ( FILE * file_pt )

inlinevirtual

C_style output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

     {
       // Number of plot points
       unsigned nplot = 5;
  
       // Output the solution
       output(file_pt, nplot);
     } // End of output

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output().

◆ output() [2/4]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output	(	FILE *	file_pt,
		const unsigned &	nplot
	)

virtual

C-style output FE representation of soln: x,y,u or x,y,z,u at nplot^SPATIAL_DIM plot points

C-style output function: x,t,u or x,y,t,u at nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Tecplot header info
     fprintf(file_pt, "%s", tecplot_zone_string(nplot).c_str());
  
     // Get the number of plot points
     unsigned num_plot_points = nplot_points(nplot);
  
     // Loop over plot points
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Loop over the coordinate directions
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Print the i-th coordinate value at local coordinate s
         fprintf(file_pt, "%g ", interpolated_x(s, i));
       }
  
       // Output the interpolated solution value at local coordinate s
       fprintf(file_pt, "%g \n", interpolated_u_ust_heat(s));
     } // for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(file_pt, nplot);
   } // End of output

References i, and s.

◆ output() [3/4]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output ( std::ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

     {
       // Number of plot points
       unsigned nplot = 5;
  
       // Output the solution
       output(outfile, nplot);
     } // End of output

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output(), and oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >::output().

◆ output() [4/4]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

virtual

Output FE representation of soln: x,y,u or x,y,z,u at nplot^SPATIAL_DIM plot points

Output function: x,t,u or x,y,t,u at nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Get the number of plot points
     unsigned num_plot_points = nplot_points(nplot);
  
     // Loop over plot points
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Loop over the coordinate directions
       for (unsigned i = 0; i < SPATIAL_DIM + 1; i++)
       {
         // Output the interpolated coordinate
         outfile << interpolated_x(s, i) << " ";
       }
  
       // Calculate the interpolated solution value
       outfile << interpolated_u_ust_heat(s) << std::endl;
     } // for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   } // End of output

References i, and s.

◆ output_element_paraview()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output_element_paraview	(	std::ofstream &	file_out,
		const unsigned &	nplot
	)

C-style output FE representation of soln: x,y,u or x,y,z,u at nplot^SPATIAL_DIM plot points

Output function: x,t,u or x,y,t,u at nplot points in each coordinate direction

   {
     // Change the scientific format so that E is used rather than e
     file_out.setf(std::ios_base::uppercase);
  
     // Make variables to hold the number of nodes and elements
     unsigned number_of_nodes = this->nplot_points_paraview(nplot);
  
     // Make variables to hold the number of elements
     unsigned total_number_of_elements = this->nsub_elements_paraview(nplot);
  
     //------------------
     // File Declaration:
     //------------------
     // Insert the necessary lines plus header of file, and
     // number of nodes and elements
     file_out << "<?xml version=\"1.0\"?>\n"
              << "<VTKFile type=\"UnstructuredGrid\" version=\"0.1\" "
              << "byte_order=\"LittleEndian\">\n"
              << "<UnstructuredGrid>\n"
              << "<Piece NumberOfPoints=\"" << number_of_nodes
              << "\" NumberOfCells=\"" << total_number_of_elements << "\">\n";
  
     //------------
     // Point Data:
     //------------
     // Check the number of degrees of freedom
     unsigned ndof = this->nscalar_paraview();
  
     // Point data is going in here
     file_out << "<PointData ";
  
     // Insert just the first scalar name, since paraview reads everything
     // else after that as being of the same type. Get information from
     // first element.
     file_out << "Scalars=\"" << this->scalar_name_paraview(0) << "\">\n";
  
     // Loop over i scalar fields and j number of elements
     for (unsigned i = 0; i < ndof; i++)
     {
       file_out << "<DataArray type=\"Float32\" "
                << "Name=\"" << this->scalar_name_paraview(i) << "\" "
                << "format=\"ascii\""
                << ">\n";
  
       // Output the i-th scalar field with nplot plot points
       this->scalar_value_paraview(file_out, i, nplot);
  
       // Close of the DataArray
       file_out << "</DataArray>\n";
     }
  
     // Close off the PointData set
     file_out << "</PointData>\n";
  
     //------------------
     // Geometric Points:
     //------------------
     // Always has to be 3 components for an unstructured grid
     file_out << "<Points>\n"
              << "<DataArray type=\"Float32\""
              << " NumberOfComponents=\"" << 3 << "\" "
              << "format=\"ascii\">\n";
  
     // Print the plot points
     this->output_paraview(file_out, nplot);
  
     // Close off the geometric points set
     file_out << "</DataArray>\n"
              << "</Points>\n";
  
     //-------
     // Cells:
     //-------
     file_out << "<Cells>\n"
              << "<DataArray type=\"Int32\" Name=\""
              << "connectivity\" format=\"ascii\">\n";
  
     // Make counter for keeping track of all the local elements,
     // because Paraview requires global coordinates
     unsigned counter = 0;
  
     // Write connectivity with the local elements
     this->write_paraview_output_offset_information(file_out, nplot, counter);
  
     // Output header stuff
     file_out << "</DataArray>\n"
              << "<DataArray type=\"Int32\" "
              << "Name=\"offsets\" format=\"ascii\">\n";
  
     // Make variable that holds the current offset number
     unsigned offset_sum = 0;
  
     // Write the offset for the specific elements
     this->write_paraview_offsets(file_out, nplot, offset_sum);
  
     // Add in header information
     file_out << "</DataArray>\n"
              << "<DataArray type=\"UInt8\" Name=\"types\">\n";
  
     // Get the type the element has
     this->write_paraview_type(file_out, nplot);
  
     // Finish off the data set
     file_out << "</DataArray>\n"
              << "</Cells>\n";
  
     //--------------
     // File Closure:
     //--------------
     file_out << "</Piece>\n"
              << "</UnstructuredGrid>\n"
              << "</VTKFile>";
   } // End of output_element_paraview

References i.

◆ output_fct() [1/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^SPATIAL_DIM plot points (time-dependent version)

Output exact solution at a given number of plot points: x,t,u_exact or x,y,t,u_exact Solution is provided via function pointer.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

   {
     // Storage for the time value
     double interpolated_t = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Vector for spatial coordinates
     Vector<double> spatial_coordinates(SPATIAL_DIM, 0.0);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution vector (here it's simply a scalar)
     Vector<double> exact_soln(1, 0.0);
  
     // Get the number of plot points
     unsigned num_plot_points = nplot_points(nplot);
  
     // Loop over plot points
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Loop over the spatial coordinates
       for (unsigned i = 0; i < SPATIAL_DIM; i++)
       {
         // Assign the i-th spatial coordinate
         spatial_coordinates[i] = interpolated_x(s, i);
  
         // Output the i-th coordinate at the point
         outfile << spatial_coordinates[i] << " ";
       }
  
       // Get the time value
       interpolated_t = interpolated_x(s, SPATIAL_DIM);
  
       // Output the time value at this point
       outfile << interpolated_t << " ";
  
       // Get the exact solution at this point
       (*exact_soln_pt)(interpolated_t, spatial_coordinates, exact_soln);
  
       // Output the exact solution at this point
       outfile << exact_soln[0] << std::endl;
     } // for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   } // End of output_fct

References ProblemParameters::exact_soln(), i, and s.

◆ output_fct() [2/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::output_fct	(	std::ostream &	outfile,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

virtual

Output exact soln: x,y,u_exact or x,y,z,u_exact at nplot^SPATIAL_DIM plot points

Output exact solution at a given number of plot points: x,t,u_exact or x,y,t,u_exact Solution is provided via function pointer.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(SPATIAL_DIM + 1, 0.0);
  
     // Vector for spatial coordinates
     Vector<double> spatial_coordinates(SPATIAL_DIM, 0.0);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution vector (here it's simply a scalar)
     Vector<double> exact_soln(1, 0.0);
  
     // Get the number of plot points
     unsigned num_plot_points = nplot_points(nplot);
  
     // Loop over plot points
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Loop over the spatial coordinates
       for (unsigned i = 0; i < SPATIAL_DIM; i++)
       {
         // Assign the i-th spatial coordinate
         spatial_coordinates[i] = interpolated_x(s, i);
  
         // Output the i-th coordinate at the point
         outfile << spatial_coordinates[i] << " ";
       }
  
       // Output the time value at this point
       outfile << interpolated_x(s, SPATIAL_DIM) << " ";
  
       // Get the exact solution at this point
       (*exact_soln_pt)(spatial_coordinates, exact_soln);
  
       // Output the exact solution at this point
       outfile << exact_soln[0] << std::endl;
     } // for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   } // End of output_fct

References ProblemParameters::exact_soln(), i, and s.

Referenced by oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >::output_fct().

◆ scalar_name_paraview()

template<unsigned SPATIAL_DIM>

std::string oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::scalar_name_paraview ( const unsigned & i ) const

inlinevirtual

Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc.

Reimplemented from oomph::FiniteElement.

     {
       // If we're outputting the solution
       if (i == 0)
       {
         // There's only one field to output
         return "U";
       }
       // Never get here
       else
       {
         std::stringstream error_stream;
         error_stream << "These unsteady heat elements only store 1 field, \n"
                      << "but i is currently  " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
  
         // Dummy return
         return " ";
       }
     } // End of scalar_name_paraview

References i, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ scalar_value_fct_paraview() [1/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::scalar_value_fct_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream << "Space-time unsteady heat elements only store a single "
                      << "field so i must be 0 rather than " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Get the number of plot points
       unsigned local_loop = this->nplot_points_paraview(nplot);
  
       // Loop over the plot points
       for (unsigned j = 0; j < local_loop; j++)
       {
         // Storage for the local coordinates
         Vector<double> s(SPATIAL_DIM + 1);
  
         // Storage for the time value
         double interpolated_t = 0.0;
  
         // Storage for the global coordinates
         Vector<double> spatial_coordinates(SPATIAL_DIM);
  
         // Get the local coordinate of the required plot point
         this->get_s_plot(j, nplot, s);
  
         // Loop over the spatial coordinates
         for (unsigned i = 0; i < SPATIAL_DIM; i++)
         {
           // Assign the i-th spatial coordinate
           spatial_coordinates[i] = interpolated_x(s, i);
         }
  
         // Get the time value
         interpolated_t = interpolated_x(s, SPATIAL_DIM);
  
         // Exact solution vector (here it's simply a scalar)
         Vector<double> exact_soln(1, 0.0);
  
         // Get the exact solution at this point
         (*exact_soln_pt)(interpolated_t, spatial_coordinates, exact_soln);
  
         // Output the interpolated solution value
         file_out << exact_soln[0] << std::endl;
       } // for (unsigned j=0;j<local_loop;j++)
     } // End of scalar_value_fct_paraview

References ProblemParameters::exact_soln(), oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), j, oomph::FiniteElement::nplot_points_paraview(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ scalar_value_fct_paraview() [2/2]

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::scalar_value_fct_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream << "Space-time unsteady heat elements only store a single "
                      << "field so i must be 0 rather than " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Get the number of plot points
       unsigned local_loop = this->nplot_points_paraview(nplot);
  
       // Loop over the plot points
       for (unsigned j = 0; j < local_loop; j++)
       {
         // Storage for the local coordinates
         Vector<double> s(SPATIAL_DIM + 1);
  
         // Storage for the global coordinates
         Vector<double> spatial_coordinates(SPATIAL_DIM);
  
         // Get the local coordinate of the required plot point
         this->get_s_plot(j, nplot, s);
  
         // Loop over the spatial coordinates
         for (unsigned i = 0; i < SPATIAL_DIM; i++)
         {
           // Assign the i-th spatial coordinate
           spatial_coordinates[i] = interpolated_x(s, i);
         }
  
         // Exact solution vector (here it's simply a scalar)
         Vector<double> exact_soln(1, 0.0);
  
         // Get the exact solution at this point
         (*exact_soln_pt)(spatial_coordinates, exact_soln);
  
         // Output the interpolated solution value
         file_out << exact_soln[0] << std::endl;
       } // for (unsigned j=0;j<local_loop;j++)
     } // End of scalar_value_fct_paraview

References ProblemParameters::exact_soln(), oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), j, oomph::FiniteElement::nplot_points_paraview(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ scalar_value_paraview()

template<unsigned SPATIAL_DIM>

void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::scalar_value_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type.

Reimplemented from oomph::FiniteElement.

     {
 #ifdef PARANOID
       if (i != 0)
       {
         std::stringstream error_stream;
         error_stream << "Space-time unsteady heat elements only store a single "
                      << "field so i must be 0 rather than " << i << std::endl;
         throw OomphLibError(
           error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Get the number of plot points
       unsigned local_loop = this->nplot_points_paraview(nplot);
  
       // Loop over the plot points
       for (unsigned j = 0; j < local_loop; j++)
       {
         // Storage for the local coordinates
         Vector<double> s(SPATIAL_DIM + 1);
  
         // Get the local coordinate of the required plot point
         this->get_s_plot(j, nplot, s);
  
         // Output the interpolated solution value
         file_out << this->interpolated_u_ust_heat(s) << std::endl;
       }
     } // End of scalar_value_paraview

References oomph::FiniteElement::get_s_plot(), i, oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_u_ust_heat(), j, oomph::FiniteElement::nplot_points_paraview(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and s.

◆ self_test()

template<unsigned SPATIAL_DIM>

unsigned oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::self_test

virtual

Self-test: Return 0 for OK.

Reimplemented from oomph::FiniteElement.

   {
     // Initialise the boolean variable
     bool passed = true;
  
     // Check lower-level stuff
     if (FiniteElement::self_test() != 0)
     {
       // If we get here then the lower-level self-tests did not pass
       passed = false;
     }
  
     // If the self-tests passed
     if (passed)
     {
       // Return the value zero
       return 0;
     }
     // If the self-tests didn't pass
     else
     {
       // Return the value one
       return 1;
     }
   } // End of self_test

References oomph::FiniteElement::self_test().

◆ shape_ust_heat()

template<unsigned SPATIAL_DIM>

virtual void oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::shape_ust_heat	(	const Vector< double > &	s,
		Shape &	psi
	)		const

protectedpure virtual

Shape functions w.r.t. to local coords.

Implemented in oomph::QUnsteadyHeatMixedOrderSpaceTimeElement< SPATIAL_DIM, NNODE_1D >.

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_u_ust_heat().

◆ source_fct_pt() [1/2]

template<unsigned SPATIAL_DIM>

SpaceTimeUnsteadyHeatSourceFctPt& oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::source_fct_pt ( )

inlinevirtual

Access function: Pointer to source function.

Implements oomph::SpaceTimeUnsteadyHeatEquationsBase.

     {
       // Return the source function pointer
       return Source_fct_pt;
     } // End of source_fct_pt

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Source_fct_pt.

Referenced by oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::further_build().

◆ source_fct_pt() [2/2]

template<unsigned SPATIAL_DIM>

SpaceTimeUnsteadyHeatSourceFctPt oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::source_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

     {
       // Return the source function pointer
       return Source_fct_pt;
     }

References oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Source_fct_pt.

◆ u_index_ust_heat()

template<unsigned SPATIAL_DIM>

virtual unsigned oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::u_index_ust_heat ( ) const

inlinevirtual

Return the index at which the unknown value is stored. The default value, 0, is appropriate for single-physics problems, when there is only one variable, the value that satisfies the unsteady heat equation. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknown is always stored at the same index at each node.

     {
       // Return the default value
       return 0;
     } // End of u_index_ust_heat

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_flux(), oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_interpolated_values(), oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_Z2_flux(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_du_dt_ust_heat(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::interpolated_u_ust_heat().

Member Data Documentation

◆ ALE_is_disabled

template<unsigned SPATIAL_DIM>

bool oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::ALE_is_disabled

protected

Boolean flag to indicate if ALE formulation is disabled when time-derivatives are computed. Only set to true if you're sure that the mesh is stationary.

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::disable_ALE(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::enable_ALE(), and oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::further_build().

◆ Alpha_pt

template<unsigned SPATIAL_DIM>

double* oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Alpha_pt

protected

Pointer to Alpha parameter (thermal inertia)

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::alpha(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::alpha_pt(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations().

◆ Beta_pt

template<unsigned SPATIAL_DIM>

double* oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Beta_pt

protected

Pointer to Beta parameter (thermal conductivity)

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::beta(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::beta_pt(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations().

◆ Default_alpha_parameter

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Default_alpha_parameter = 1.0

staticprivate

Default value for Alpha parameter (thermal inertia)

Static default value for the Alpha parameter (thermal inertia): One for natural scaling

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations().

◆ Default_beta_parameter

template<unsigned SPATIAL_DIM>

double oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Default_beta_parameter = 1.0

staticprivate

Default value for Beta parameter (thermal conductivity)

Static default value for the Beta parameter (thermal conductivity): One for natural scaling

Referenced by oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::SpaceTimeUnsteadyHeatMixedOrderEquations().

◆ Source_fct_pt

template<unsigned SPATIAL_DIM>

SpaceTimeUnsteadyHeatSourceFctPt oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::Source_fct_pt

protected

Pointer to source function:

Referenced by oomph::RefineableSpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::further_build(), oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::get_source_ust_heat(), and oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >::source_fct_pt().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned SPATIAL_DIM> class oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >

Constructor & Destructor Documentation

◆ SpaceTimeUnsteadyHeatMixedOrderEquations() [1/2]

◆ SpaceTimeUnsteadyHeatMixedOrderEquations() [2/2]

Member Function Documentation

◆ alpha()

◆ alpha_pt()

◆ beta()

◆ beta_pt()

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ compute_norm()

◆ disable_ALE()

◆ dshape_and_dtest_eulerian_at_knot_ust_heat()

◆ dshape_and_dtest_eulerian_ust_heat()

◆ dshape_local_ust_heat()

◆ dtest_local_ust_heat()

◆ du_dt_ust_heat()

◆ enable_ALE()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_ust_heat()

◆ get_flux()

◆ get_source_ust_heat()

◆ interpolated_du_dt_ust_heat()

◆ interpolated_u_ust_heat() [1/2]

◆ interpolated_u_ust_heat() [2/2]

◆ nscalar_paraview()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_element_paraview()

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ scalar_name_paraview()

◆ scalar_value_fct_paraview() [1/2]

◆ scalar_value_fct_paraview() [2/2]

◆ scalar_value_paraview()

◆ self_test()

◆ shape_ust_heat()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u_index_ust_heat()

Member Data Documentation

◆ ALE_is_disabled

◆ Alpha_pt

◆ Beta_pt

◆ Default_alpha_parameter

◆ Default_beta_parameter

◆ Source_fct_pt

template<unsigned SPATIAL_DIM>
class oomph::SpaceTimeUnsteadyHeatMixedOrderEquations< SPATIAL_DIM >