Approximation

Collaboration diagram for Approximation:

Modules
	Standard Linear Approximation
Defines
#define	APC_TRUE 1
#define	APC_FALSE 0
#define	APC_MAXELP_COMP 5
#define	APC_MAXELP_TENS 505
#define	APC_MAXELVD 130
#define	APC_MAXELSD 300
#define	APC_DOUBLE_MAXELSD 600
#define	APC_MAX_GEO_DOFS 18
#define	APC_CUR_FIELD_ID 0
#define	APC_NO_DOFS -1
#define	APC_BASE_TENSOR_DG 1
#define	APC_BASE_COMPLETE_DG 2
#define	APC_BASE_PRISM_STD 3
#define	APC_BASE_PRISM_QUAD_STD 32
#define	APC_BASE_TETRA_STD 4
#define	APC_BASE_TETRA_QUAD_STD 42
#define	APC_ZERO 0
#define	APC_READ 1
#define	APC_INIT 2
#define	APC_ELEMENT 4
#define	APC_FACE 3
#define	APC_EDGE 2
#define	APC_VERTEX 1
#define	APC_MIXED_ELEMENT 8
#define	APC_MIXED_FACE 7
#define	APC_MIXED_EDGE 6
#define	APC_MIXED_VERTEX 5
#define	APC_MIXED_NO_SEC_FIELD -1
#define	APC_NO_COMP 0
#define	APC_COMP_SM 1
#define	APC_COMP_RHS 2
#define	APC_COMP_BOTH 3
#define	APC_COMP_MM 10
#define	APC_REWR_SM 4
#define	APC_REWR_RHS 5
#define	APC_REWR_BOTH 6
#define	APC_REWR_MM 13
#define	APC_REF_ALLOWED 1
#define	APC_REF_DENIED 2
#define	APC_DEREF_ALLOWED 3
#define	APC_DEREF_DENIED 4
#define	APC_LINEAR_APPROXIMATION_PDEG 1
#define	APC_QUADRATIC_HIERACHICAL_APPROXIMATION_PDEG 15
#define	APC_QUADRATIC_APPROXIMATION_PDEG 2
#define	APC_MIXED_P1_P1_APPROXIMATION_PDEG 11
#define	APC_MIXED_P2_P1_APPROXIMATION_PDEG 21
#define	APC_MIXED_P2_P2_APPROXIMATION_PDEG 22
#define	APC_P1_NONE_G1 101
#define	APC_P15_NONE_G1 151
#define	APC_P2_NONE_G1 201
#define	APC_P2_NONE_G2 202
#define	APC_P1_P1_G1 111
#define	APC_P2_P2_G2 222
#define	APC_P2_P1_G2 212
#define	APC_P2_P1_G1 211
#define	APC_TETRA_NUM_SHAP_LINEAR_APROXIMATION 4
#define	APC_TETRA_NUM_SHAP_QUADRATIC_APROXIMATION 10
#define	APC_PRISM_NUM_SHAP_LINEAR_APROXIMATION 6
#define	APC_PRISM_NUM_SHAP_QUADRATIC_APROXIMATION 18
#define	APC_PRISM_NUM_SHAP_HIERARCHICAL_QUADRATIC_APROXIMATION 15
#define	APC_MAX_CONSTR_EL_LOC 10
#define	APC_CLOSE 1.0e-6
#define	APC_SMALL 1.0e-9
#define	APC_ELEM_CALC_SHAPE_FUNC_N_VALUES 1
#define	APC_ELEM_CALC_DERIVATIVES_AND_JACOBIAN 2
#define	APC_ELEM_CALC_ON_FACE(face_number) 3+face_number
Enumerations
enum	ape_sol_xglob { APE_SOL_XGLOB_DEFAULT = 0x00, APE_SOL_XGLOB_MATCH_ALL_ELEMENTS = 0x01, APE_SOL_XGLOB_MATCH_WITH_ADAPTATION = 0x02, APE_SOL_XGLOB_CHECK_ONLY_GIVEN_ELEMENT = 0x04 }
	Flags controling apr_sol_xglob. More...
Functions
int	apr_module_introduce (char *Approx_name)
int	apr_init_field (char Field_type, int Control, int Mesh_id, int Nreq, int Nr_sol, int Pdeg_in, char Filename, double(Fun_p)(int, double *, int))
int	apr_write_field (int Field_id, int Nreq, int Select, double Accuracy, char *Filename)
int	apr_check_field (int Field_id)
int	apr_get_mesh_id (int Field_id)
int	apr_get_mixed_second_field_id (int Field_id)
int	apr_get_nreq (int Field_id)
int	apr_get_mixed_nreq (int Field_id)
int	apr_get_nr_sol (int Field_id)
int	apr_get_el_pdeg_numshap (int Field_id, int El_id, int *Pdeg_vec)
int	apr_get_el_pdeg_numshap_related_with_dof_type (int Field_id, int El_id, int Dof_type, int *Pdeg)
int	apr_get_base_type (int Field_id, int El_id)
int	apr_get_ent_pdeg (int Field_id, int Ent_type, int Ent_id)
int	apr_set_ent_pdeg (int Field_id, int Ent_type, int Ent_id, int Pdeg)
int	apr_get_el_pdeg (int Field_id, int El_id, int *Pdeg_vec)
int	apr_set_el_pdeg (int Field_id, int El_id, int *Pdeg)
int	apr_get_mixed_pdeg (int Field_id, int *Pdeg_vec)
int	apr_get_el_geo_pdeg (int Field_id, int El_id, int *Pdeg_vec)
int	apr_set_el_geo_pdeg (int Field_id, int El_id, int *Pdeg_vec)
int	apr_move_node (int Field_id, int Node_id, int Node_type, double *Shift_vec)
int	apr_node_coor (int Field_id, int Node_id, int Node_type, double *coord)
int	apr_get_el_dofs (int Field_id, int El_id, int Vect_id, double *El_dofs_std)
int	apr_get_el_geo_dofs (int Field_id, int El_id, int GeoDofs_id, int GeoDofs_type, double *GeoDofs)
int	apr_get_ent_numshap (int Field_id, int Ent_type, int Ent_id)
int	apr_get_ent_nrdofs (int Field_id, int Ent_type, int Ent_id)
int	apr_get_nrdofs_glob (int Field_id)
int	apr_read_ent_dofs (int Field_id, int Ent_type, int Ent_id, int Ent_nrdofs, int Vect_id, double *Vect_dofs)
int	apr_write_ent_dofs (int Field_id, int Ent_type, int Ent_id, int Ent_nrdofs, int Vect_id, double *Vect_dofs)
int	apr_create_ent_dofs (int Field_id, int Ent_type, int Ent_id, int Ent_nrdofs, int Vect_id, double *Vect_dofs)
int	apr_set_ini_con (int Field_id, double(Fun_p)(int, double , int))
int	apr_prepare_integration_parameters (int Field_id, int El_id, int Geo_order, int Num_geo_dofs, double Geo_dofs, int El_mate, int Base, int Pdeg_vec, int Num_shap, int Nreq, int *Num_dofs)
int	apr_num_int_el (int Problem_id, int Field_id, int El_id, int Comp_sm, int Pdeg_vec, double Sol_dofs_k, double Sol_dofs_n, int diagonal, double Stiff_mat, double Rhs_vect)
int	apr_get_stiff_mat_data (int Field_id, int El_id, int Comp_sm, char Transpose, int Pdeg_in, int Nreq_in, int Nr_dof_ent, int List_dof_ent_type, int List_dof_ent_id, int List_dof_ent_nrdofs, int Nrdofs_loc, double Stiff_mat, double *Rhs_vect)
int	apr_proj_dof_ref (int Field_id, int El, int Max_elem_id, int Max_face_id, int Max_edge_id, int Max_vert_id)
int	apr_rewr_sol (int Field_id, int Sol_from, int Sol_to)
int	apr_free_field (int Field_id)
int	apr_limit_deref (int Field_id, int El_id)
int	apr_limit_ref (int Field_id, int El_id)
int	apr_refine (int Field_id, int El_id)
int	apr_derefine (int Field_id, int El_id)
int	apr_shape_fun_3D (int Base_type, int Pdeg, double Eta, double Base_phi, double Base_dphix, double Base_dphiy, double *Base_dphiz)
double	apr_elem_calc_3D (int Control, int Nreq, int Pdeg_vec, int Base_type, double Eta, double Node_coor, double Sol_dofs, double Base_phi, double Base_dphix, double Base_dphiy, double Base_dphiz, double Xcoor, double Sol, double Dsolx, double Dsoly, double Dsolz, double Vec_nor)
int	apr_set_quadr_3D (int Base_type, int Pdeg_vec, int Ngauss, double Xg, double Wg)
int	apr_set_quadr_2D (int Fa_type, int Base_type, int Pdeg_vec, int Ngauss, double Xg, double Wg)
int	apr_set_quadr_2D_penalty (int Fa_type, int Base_type, int Pdeg_vec, int Ngauss, double Xg, double Wg)
int	apr_L2_proj (int Field_id, int Mode, int El, int Pdeg_vec, double Dofs, int El_from, int Pdeg_vec_from, double Dofs_from, double(Fun_p)(double , double , double , double ))
int	apr_sol_xglob (int Field_id, double Xglob, int Nb_sol, int El, double Xloc, double Sol, double Dxsol, double Dysol, double *Dzsol, double Close_proximity_precision, int Sol_xglob_flags)
int	apr_create_constr_data (int Field_id)
int	apr_get_el_constr_data (int Field_id, int El_id, int Nodes, int Nr_constr, int Constr_id, int Constr_type, double *Constr_val)
int	apr_get_constr_data (int Field_id, int Node_id, int Node_type, int Constr, int Constr_type)
int	apr_get_profile (FILE filePtr, int fieldId, int solNr, int nSol, double pt1, double *pt2, int nPoints)
	apr_get_profile - to return values of solution at given points

Define Documentation

#define APC_BASE_COMPLETE_DG 2

#define APC_BASE_PRISM_QUAD_STD 32

#define APC_BASE_PRISM_STD 3

#define APC_BASE_TENSOR_DG 1

Basis functions types

#define APC_BASE_TETRA_QUAD_STD 42

#define APC_BASE_TETRA_STD 4

#define APC_CLOSE 1.0e-6

Close proximity precision /* how close to the boundary is on the boundary

#define APC_COMP_BOTH 3

#define APC_COMP_MM 10

#define APC_COMP_RHS 2

#define APC_COMP_SM 1

#define APC_CUR_FIELD_ID 0

#define APC_DEREF_ALLOWED 3

#define APC_DEREF_DENIED 4

#define APC_DOUBLE_MAXELSD 600

#define APC_EDGE 2

#define APC_ELEM_CALC_DERIVATIVES_AND_JACOBIAN 2

#define APC_ELEM_CALC_ON_FACE ( face_number ) 3+face_number

#define APC_ELEM_CALC_SHAPE_FUNC_N_VALUES 1

#define APC_ELEMENT 4

Identifiers of mesh entities

#define APC_FACE 3

#define APC_FALSE 0

#define APC_INIT 2

#define APC_LINEAR_APPROXIMATION_PDEG 1

approximation field type

#define APC_MAX_CONSTR_EL_LOC 10

#define APC_MAX_GEO_DOFS 18

maximal number of geo dofs

#define APC_MAXELP_COMP 5

maximal degree of polynomial for an element

#define APC_MAXELP_TENS 505

#define APC_MAXELSD 300

maximal number of scalar dofs (nreq*num_shap) e.g. 4*15=60 for quadratic prisms and ns_supg

#define APC_MAXELVD 130

maximal number of vector dofs (shape functions) for an element

#define APC_MIXED_EDGE 6

#define APC_MIXED_ELEMENT 8

#define APC_MIXED_FACE 7

#define APC_MIXED_NO_SEC_FIELD -1

#define APC_MIXED_P1_P1_APPROXIMATION_PDEG 11

#define APC_MIXED_P2_P1_APPROXIMATION_PDEG 21

#define APC_MIXED_P2_P2_APPROXIMATION_PDEG 22

#define APC_MIXED_VERTEX 5

#define APC_NO_COMP 0

Options for assembling - should not be changed !!!

#define APC_NO_DOFS -1

degree of approximation symbol indicating not allocated dofs

#define APC_P15_NONE_G1 151

#define APC_P1_NONE_G1 101

unified approximation pdeg [geo + base]

#define APC_P1_P1_G1 111

#define APC_P2_NONE_G1 201

#define APC_P2_NONE_G2 202

#define APC_P2_P1_G1 211

#define APC_P2_P1_G2 212

#define APC_P2_P2_G2 222

#define APC_PRISM_NUM_SHAP_HIERARCHICAL_QUADRATIC_APROXIMATION 15

#define APC_PRISM_NUM_SHAP_LINEAR_APROXIMATION 6

#define APC_PRISM_NUM_SHAP_QUADRATIC_APROXIMATION 18

#define APC_QUADRATIC_APPROXIMATION_PDEG 2

#define APC_QUADRATIC_HIERACHICAL_APPROXIMATION_PDEG 15

#define APC_READ 1

#define APC_REF_ALLOWED 1

symbols for defining whether refinements/derefinements should be allowed e.g. due to mesh regularity constraints

#define APC_REF_DENIED 2

#define APC_REWR_BOTH 6

#define APC_REWR_MM 13

#define APC_REWR_RHS 5

#define APC_REWR_SM 4

#define APC_SMALL 1.0e-9

#define APC_TETRA_NUM_SHAP_LINEAR_APROXIMATION 4

aproximation number of shape function for element type

#define APC_TETRA_NUM_SHAP_QUADRATIC_APROXIMATION 10

#define APC_TRUE 1

#define APC_VERTEX 1

#define APC_ZERO 0

Initialization options

Enumeration Type Documentation

enum ape_sol_xglob

Flags controling apr_sol_xglob.

Enumerator:

APE_SOL_XGLOB_DEFAULT	the defaults are: not APE_SOL_XGLOB_MATCH_ALL_ELEMENTS = match first element only not APE_SOL_XGLOB_MATCH_WITH_ADAPTATION = match only at initial level not APE_SOL_XGLOB_CHECK_ONLY_GIVEN_ELEMENT = search for matching element(s)
APE_SOL_XGLOB_MATCH_ALL_ELEMENTS
APE_SOL_XGLOB_MATCH_WITH_ADAPTATION
APE_SOL_XGLOB_CHECK_ONLY_GIVEN_ELEMENT	if the element containing given point is already known, one can put its' id into El[0] and only this element will be considered

Function Documentation

int apr_check_field ( int Field_id )

----------------------------------------------------------- apr_check_field - to check approximation field data structure ------------------------------------------------------------

Parameters:

Field_id

in: approximation field ID

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int apr_create_constr_data ( int Field_id )

----------------------------------------------------------- apr_create_constr_data - to create and fill constraint arrays (assuming approximation and mesh data agree) ------------------------------------------------------------

Parameters:

Field_id

returns: >=0 - success code, <0 - error code in: approximation field ID

int apr_create_ent_dofs	(	int	Field_id,
		int	Ent_type,
		int	Ent_id,
		int	Ent_nrdofs,
		int	Vect_id,
		double *	Vect_dofs
	)

----------------------------------------------------------- apr_create_ent_dofs - to write a vector of dofs associated with a given mesh entity to approximation field data structure ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity
	Ent_nrdofs	in: mesh entity ID
	Vect_id	in: number of dofs associated with the entity
	Vect_dofs	in: vector ID in case of multiple solution vectors in: dofs to be written

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int apr_derefine	(	int	Field_id,
		int	El_id
	)

----------------------------------------------------------- apr_derefine - to derefine an element or the whole mesh with irregularity check ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	El_id	in: mesh ID or 0 (MMC_CUR_MESH_ID) for the current mesh in: element ID or -2 (MMC_DO_UNI_DEREF) for uniform derefinement

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double apr_elem_calc_3D	(	int	Control,
		int	Nreq,
		int *	Pdeg_vec,
		int	Base_type,
		double *	Eta,
		double *	Node_coor,
		double *	Sol_dofs,
		double *	Base_phi,
		double *	Base_dphix,
		double *	Base_dphiy,
		double *	Base_dphiz,
		double *	Xcoor,
		double *	Sol,
		double *	Dsolx,
		double *	Dsoly,
		double *	Dsolz,
		double *	Vec_nor
	)

----------------------------------------------------------------- apr_elem_calc_3D - to perform element calculations (to provide data on coordinates, solution, shape functions, etc. for a given point inside element (given local coordinates Eta[i]); for geometrically multi-linear or linear 3D elements -------------------------------------------------------------------

Parameters:

	Control	returns: Jacobian determinant at a point, either for volume integration if Vec_norm==NULL, or for surface integration otherwise
	Nreq	in: control parameter (what to compute): APC_ELEM_CALC_ON_FACE(face_number) >2 - computations on the
	Pdeg_vec	in: number of equations
	Base_type	in: element degree of polynomial
	Eta	in: type of basis functions: define APC_BASE_TENSOR_DG 1 define APC_BASE_COMPLETE_DG 2 define APC_BASE_PRISM_STD 3 // for prismatic elements define APC_BASE_PRISM_QUAD_STD 32 // for quadratic prismatic elements [element type 3 / approximation degree 2] define APC_BASE_TETRA_STD 4 // for tetrahedral elements define APC_BASE_TETRA_QUAD_STD 42 // for quadratic tetrahedral elements [element type 4 / approximation degree 2]
	Node_coor	in: local coordinates of the input point
	Sol_dofs	in: array of coordinates of vertices of element
	Base_phi	in: array of element' dofs
	Base_dphix	out: basis functions
	Base_dphiy	out: x-derivatives of basis functions
	Base_dphiz	out: y-derivatives of basis functions
	Xcoor	out: z-derivatives of basis functions
	Sol	out: global coordinates of the point
	Dsolx	out: solution at the point
	Dsoly	out: derivatives of solution at the point
	Dsolz	out: derivatives of solution at the point
	Vec_nor	out: derivatives of solution at the point out: outward unit vector normal to the face

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int apr_free_field ( int Field_id )

----------------------------------------------------------- apr_free_field - to free approximation field data structure ------------------------------------------------------------

Parameters:

Field_id

in: approximation field ID

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int apr_get_base_type	(	int	Field_id,
		int	El_id
	)

-------------------------------------------------------- apr_get_base_type - to return the type of basis functions for an element REMARK: type of basis functions differentiates element types as well examples for discontinuous Galerkin approximation (from include/aph_intf.h): define APC_BASE_TENSOR_DG 1 define APC_BASE_COMPLETE_DG 2 examples for standard linear approximation (from include/aph_intf.h): define APC_BASE_PRISM_STD 3 // for linear prismatic elements define APC_BASE_TETRA_STD 4 // for linear tetrahedral elements ---------------------------------------------------------

Parameters:

	Field_id	returns: >0 - type of basis functions, <0 - error code
	El_id	in: field ID in: element ID

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int apr_get_constr_data	(	int	Field_id,
		int	Node_id,
		int	Node_type,
		int *	Constr,
		int *	Constr_type
	)

----------------------------------------------------------- apr_get_constr_data - to return constraints data for a node (dof entity) ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Node_id	in: approximation field ID
	Node_type	in: id of node (can be vertex or edge)
	Constr	in: type of input node APC_VERTEX or APC_EDGE
	Constr_type	out: table of constraints data, Constr[0] - number of constraints (in linear approximation 2 - mid-edge node, 4 - mid-side node) out: table of constraints element type, Constr_type[0] - id of coefficient vector

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int apr_get_el_constr_data	(	int	Field_id,
		int	El_id,
		int *	Nodes,
		int *	Nr_constr,
		int *	Constr_id,
		int *	Constr_type,
		double *	Constr_val
	)

----------------------------------------------------------- apr_get_el_constr_data - to return the number and the list of element's real nodes, with the corresponding constraint coefficients ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	El_id	in: approximation field ID
	Nodes	in: element ID
	Nr_constr	out: list of vertex node IDs
	Constr_id	out: list with the numbers of constraints for each vertex
	Constr_type	out: ID's of parent (constraining) nodes
	Constr_val	out: Type of parent (used in quadratic approximation and above) out: the corresponding constraint coefficients

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int apr_get_el_dofs	(	int	Field_id,
		int	El_id,
		int	Vect_id,
		double *	El_dofs_std
	)

----------------------------------------------------------- apr_get_el_dofs - to return the list of standard dofs for a given element each dof corresponds to a standard shape function ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - the number of dofs <0 - error code
	El_id	in: approximation field ID
	Vect_id	in: element ID
	El_dofs_std	in: vector ID in case of multiple solution vectors out: the list of values of element dofs

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int apr_get_el_geo_dofs	(	int	Field_id,
		int	El_id,
		int *	GeoDofs_id,
		int *	GeoDofs_type,
		double *	GeoDofs
	)

----------------------------------------------------------- apr_get_el_geo_dofs - to get geometric coordinates for a given element ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - the number of dofs <0 - error code
	El_id	in: approximation field ID
	GeoDofs_id	in: element ID
	GeoDofs_type	out: list of dofs in element
	GeoDofs	out: type of dofs [APC_VERTEX / APC_EDGE / APC_FACE]

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int apr_get_el_geo_pdeg	(	int	Field_id,
		int	El_id,
		int *	Pdeg_vec
	)

----------------------------------------------------------- apr_get_el_geo_pdeg - to return the degree of approximation associated with geometric transformation of element ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code, <0 - error code
	El_id	in: approximation field ID
	Pdeg_vec	in: element ID out: degree of approximation symbol

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int apr_get_el_pdeg	(	int	Field_id,
		int	El_id,
		int *	Pdeg_vec
	)

----------------------------------------------------------- apr_get_el_pdeg - to return the degree of approximation vector associated with a given element ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code <0 - error code
	El_id	in: approximation field ID
	Pdeg_vec	in: element ID out: degree of approximation symbol or vector

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int apr_get_el_pdeg_numshap	(	int	Field_id,
		int	El_id,
		int *	Pdeg_vec
	)

-------------------------------------------------------- apr_get_el_pdeg_numshap - to return the number of shape functions (scalar DOFs) for an element given its degree of approximation symbol or vector pdeg ---------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	El_id	in: field ID
	Pdeg_vec	in: element ID in: degree of approximation symbol or vector

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int apr_get_el_pdeg_numshap_related_with_dof_type	(	int	Field_id,
		int	El_id,
		int	Dof_type,
		int *	Pdeg
	)

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int apr_get_ent_nrdofs	(	int	Field_id,
		int	Ent_type,
		int	Ent_id
	)

----------------------------------------------------------- apr_get_ent_nrdofs - to return the number of dofs associated with a given mesh entity ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - the number of dofs, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity in: mesh entity ID

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int apr_get_ent_numshap	(	int	Field_id,
		int	Ent_type,
		int	Ent_id
	)

----------------------------------------------------------- apr_get_ent_numshap - to return the number of shape functions (vector DOFs) associated with a given mesh entity ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - the number of dofs, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity in: mesh entity ID

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int apr_get_ent_pdeg	(	int	Field_id,
		int	Ent_type,
		int	Ent_id
	)

----------------------------------------------------------- apr_get_ent_pdeg - to return the degree of approximation symbol associated with a given mesh entity ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - approximation index for P1 and P2, 0 - dof entity inactive (constrained) or aproximation index in P0 <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity in: mesh entity ID

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int apr_get_mesh_id ( int Field_id )

----------------------------------------------------------- apr_get_mesh_id - to return the ID of the associated mesh ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - ID of the associated mesh, <0 - error code in: approximation field ID

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int apr_get_mixed_nreq ( int Field_id )

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int apr_get_mixed_pdeg	(	int	Field_id,
		int *	Pdeg_vec
	)

----------------------------------------------------------- apr_get_mixed_pdeg - to get approximation pdeg associated with first or second field in mixed approximation ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code, <0 - error code
	Pdeg_vec	in: approximation field ID out: degree of approximation symbol

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int apr_get_mixed_second_field_id ( int Field_id )

----------------------------------------------------------- apr_get_mixed_second_field_id - to return ID of second field in mixed approximation ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - ID of the associated second field id in mixed, <0 - error code in: approximation primary field ID

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int apr_get_nr_sol ( int Field_id )

----------------------------------------------------------- apr_get_nr_sol - to return the number of solution vectors stored ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - number of solution vectors, <0 - error code in: approximation field ID

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int apr_get_nrdofs_glob ( int Field_id )

-------------------------------------------------------- apr_get_nrdofs_glob - to return a global dimension of the problem ---------------------------------------------------------

Parameters:

Field_id

returns: global dimension of the problem in: field ID

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int apr_get_nreq ( int Field_id )

----------------------------------------------------------- apr_get_nreq - to return the number of components in solution vector ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - number of solution components, <0 - error code in: approximation field ID

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int apr_get_profile	(	FILE *	filePtr,
		int	fieldId,
		int	solNr,
		int	nSol,
		double *	pt1,
		double *	pt2,
		int	nPoints
	)

apr_get_profile - to return values of solution at given points

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int apr_get_stiff_mat_data	(	int	Field_id,
		int	El_id,
		int	Comp_sm,
		char	Transpose,
		int	Pdeg_in,
		int	Nreq_in,
		int *	Nr_dof_ent,
		int *	List_dof_ent_type,
		int *	List_dof_ent_id,
		int *	List_dof_ent_nrdofs,
		int *	Nrdofs_loc,
		double *	Stiff_mat,
		double *	Rhs_vect
	)

----------------------------------------------------------- apr_get_stiff_mat_data - to return data on dof entities for an element and to compute or rewrite element's stiffness matrix and RHSV ------------------------------------------------------------

Parameters:

	El_id	in: approximation field ID
	Comp_sm	in: unique identifier of the element
	Transpose	in: indicator for the scope of computations: APC_NO_COMP - do not compute anything APC_COMP_SM - compute entries to stiff matrix only APC_COMP_RHS - compute entries to rhs vector only APC_COMP_BOTH - compute entries for sm and rhsv APC_REWR_SM - rewrite only entries to stiff matrix only APC_REWR_RHS - rewrite only entries to rhs vector only APC_REWR_BOTH - rewrite only entries for sm and rhsv
	Pdeg_in	in: perform transposition while rewriting 'y' or 'Y' - yes, otherwise - no
	Nreq_in	in: enforced degree of polynomial (if > 0 )
	Nr_dof_ent	in: enforced nreq (if > 0 )
	List_dof_ent_type	in: size of arrays, out: no of filled entries, i.e. number of mesh entities with which dofs and stiffness matrix blocks are associated
	List_dof_ent_id	out: list of no of dofs for 'dof' entity
	List_dof_ent_nrdofs	out: list of no of dofs for 'dof' entity
	Nrdofs_loc	out: list of no of dofs for 'dof' entity
	Stiff_mat	in(optional): size of Stiff_mat and Rhs_vect out(optional): actual number of dofs per integration entity
	Rhs_vect	out(optional): stiffness matrix stored columnwise out(optional): rhs vector

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int apr_init_field	(	char	Field_type,
		int	Control,
		int	Mesh_id,
		int	Nreq,
		int	Nr_sol,
		int	Pdeg_in,
		char *	Filename,
		double()(int, double , int)	Fun_p
	)

----------------------------------------------------------- apr_init_field - to initiate new approximation field and read its control parameters ------------------------------------------------------------

Parameters:

	Field_type	returns: >0 - field ID, <0 - error code
	Control	options: s - standard c - discontinuous with complete basis t - discontinuous with tensor product basis
	Mesh_id	in: control variable: APC_INIT - to initialize the field to zero APC_READ - to read field values from the file APC_INIT - to initialize the field using function provided by the problem dependent module
	Nreq	in: ID of the corresponding mesh
	Nr_sol	in: number of equations - solution vector components
	Pdeg_in	in: number of solution vectors for each dof entity
	Filename	in: degree of approximating polynomial and geometry in format [psg] p - primary field degree / s - secondary field degree for mixe default 0 / g - geometry
	Fun_p	in: name of the file to read approximation data pointer to function that provides problem dependent initial condition data

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int apr_L2_proj	(	int	Field_id,
		int	Mode,
		int	El,
		int *	Pdeg_vec,
		double *	Dofs,
		int *	El_from,
		int *	Pdeg_vec_from,
		double *	Dofs_from,
		double()(double , double , double , double *)	Fun_p
	)

-------------------------------------------------------- apr_L2_proj - to L2 project a function onto an element ---------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success, <=0 - failure
	Mode	in: field ID
	El	in: mode of operation <-1 - projection from ancestor to father the value is the number of ancestors -1 - projection from father to son >0 - projection of function, the value is a flag for routine returning function value at point
	Pdeg_vec	in: element number
	Dofs	in: element degree of approximation
	El_from	out: workspace for degress of freedom of El NULL - write to data structure
	Pdeg_vec_from	in: list of elements to provide function
	Dofs_from	in: degree of polynomial for each El_from if element Pdeg is a vector - its components must be suitably placed in Pdeg_vec_from
	Fun_p	in: Dofs of El_from or... in: pointer to function with field values and its derivatives

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int apr_limit_deref	(	int	Field_id,
		int	El_id
	)

----------------------------------------------------------- apr_limit_deref - to return whether derefinement is allowed or not the routine does not use approximation data structures but the result depends on the approximation method ------------------------------------------------------------

Parameters:

El_id

in: approximation field ID in: unique identifier of the element

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int apr_limit_ref	(	int	Field_id,
		int	El_id
	)

----------------------------------------------------------- apr_limit_ref - to return whether refinement is allowed or not the routine does not use approximation data structures but the result depends on the approximation method ------------------------------------------------------------

Parameters:

El_id

in: approximation field ID in: unique identifier of the element

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int apr_module_introduce ( char * Approx_name )

----------------------------------------------------------- apr_module_introduce - to return the approximation method's name ------------------------------------------------------------

Parameters:

Approx_name

returns: >=0 - success code, <0 - error code out: the name of the approximation method

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int apr_move_node	(	int	Field_id,
		int	Node_id,
		int	Node_type,
		double *	Shift_vec
	)

----------------------------------------------------------- apr_move_node - to move real geometric node by vector, node is related to vertex / edge or face ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - success code, <0 - error code

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int apr_node_coor	(	int	Field_id,
		int	Node_id,
		int	Node_type,
		double *	coord
	)

----------------------------------------------------------- apr_node_coor - to return node cordinates related to vertices / edges or faces ------------------------------------------------------------

Parameters:

Field_id

returns: >0 - success code, <0 - error code

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int apr_num_int_el	(	int	Problem_id,
		int	Field_id,
		int	El_id,
		int	Comp_sm,
		int *	Pdeg_vec,
		double *	Sol_dofs_k,
		double *	Sol_dofs_n,
		int *	diagonal,
		double *	Stiff_mat,
		double *	Rhs_vect
	)

----------------------------------------------------------- apr_num_int_el - to perform numerical integration for an element ------------------------------------------------------------

!!!!! OLD OBSOLETE VERSION !!!!!!

----------------------------------------------------------------------!

--------------------- LOOP OVER GAUSS POINTS -------------------------!

----------------------------------------------------------------------!

!!!!! OLD OBSOLETE VERSION !!!!!!

----------------------------------------------------------------------!

--------------------- LOOP OVER GAUSS POINTS -------------------------!

----------------------------------------------------------------------!

Parameters:

	El_id	in: approximation field ID
	Comp_sm	in: unique identifier of the element
	Pdeg_vec	in: indicator for the scope of computations: APC_NO_COMP - do not compute anything APC_COMP_SM - compute entries to stiff matrix only APC_COMP_RHS - compute entries to rhs vector only APC_COMP_BOTH - compute entries for sm and rhsv
	Sol_dofs_k	in: enforced degree of polynomial (if !=NULL )
	Sol_dofs_n	in: solution dofs from previous iteration (for nonlinear problems)
	diagonal	in: solution dofs from previous time step (for nonlinear problems)
	Stiff_mat	array of indicators whether coefficient matrices are diagonal
	Rhs_vect	out: stiffness matrix stored columnwise out: rhs vector

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int apr_prepare_integration_parameters	(	int	Field_id,
		int	El_id,
		int *	Geo_order,
		int *	Num_geo_dofs,
		double *	Geo_dofs,
		int *	El_mate,
		int *	Base,
		int *	Pdeg_vec,
		int *	Num_shap,
		int *	Nreq,
		int *	Num_dofs
	)

----------------------------------------------------------- apr_prepare_integration_parameters - used e.g. by apr_num_int_el ------------------------------------------------------------

Parameters:

	El_id	in: approximation field ID
	Geo_order	in: element ID
	Num_geo_dofs	out: geometrical order of approximation
	Geo_dofs	out: number of geometrical degrees of freedom
	El_mate	out: geometrical degrees of freedom
	Base	out: material index (in materials database)
	Pdeg_vec	out: type of basis functions
	Num_shap	out: degree of approximation symbol or vector
	Nreq	out: number of shape functions
	Num_dofs	out: number of components for unknowns out: number of scalar dofs (num_dofs = nreq*num_shap)

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int apr_proj_dof_ref	(	int	Field_id,
		int	El,
		int	Max_elem_id,
		int	Max_face_id,
		int	Max_edge_id,
		int	Max_vert_id
	)

----------------------------------------------------------- apr_proj_dof_ref - to rewrite dofs after modifying the mesh ------------------------------------------------------------

Parameters:

	El	in: approximation field ID
	Max_elem_id	in: >0 - rewrite after one [de]refinement of el <=0 - rewrite after massive [de]refinements
	Max_face_id	in: maximal element (face, etc.) id
	Max_edge_id	before and after refinements

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int apr_read_ent_dofs	(	int	Field_id,
		int	Ent_type,
		int	Ent_id,
		int	Ent_nrdofs,
		int	Vect_id,
		double *	Vect_dofs
	)

----------------------------------------------------------- apr_read_ent_dofs - to read a vector of dofs associated with a given mesh entity from approximation field data structure ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity
	Ent_nrdofs	in: mesh entity ID
	Vect_id	in: number of dofs associated with the entity
	Vect_dofs	in: vector ID in case of multiple solution vectors out: dofs read from data structure

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int apr_refine	(	int	Field_id,
		int	El_id
	)

----------------------------------------------------------- apr_refine - to refine an element or the whole mesh checking mesh irregularity ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	El_id	in: field ID in: element ID or -1 (MMC_DO_UNI_REF) for uniform refinement

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int apr_rewr_sol	(	int	Field_id,
		int	Sol_from,
		int	Sol_to
	)

----------------------------------------------------------- apr_rewr_sol - to rewrite solution from one vector to another ------------------------------------------------------------

Parameters:

	Sol_from	in: data structure to be used
	Sol_to	in: ID of vector to read solution from in: ID of vector to write solution to

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int apr_set_el_geo_pdeg	(	int	Field_id,
		int	El_id,
		int *	Pdeg_vec
	)

----------------------------------------------------------- apr_set_el_geo_pdeg - to set the degree of approximation associated with geometric transformation of element ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code, <0 - error code
	El_id	in: approximation field ID
	Pdeg_vec	in: element ID in: degree of approximation symbol

int apr_set_el_pdeg	(	int	Field_id,
		int	El_id,
		int *	Pdeg
	)

----------------------------------------------------------- apr_set_el_pdeg - to set the degree of approximation vector associated with a given element ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code, <0 - error code
	El_id	in: approximation field ID
	Pdeg	in: element ID out: degree of approximation symbol

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int apr_set_ent_pdeg	(	int	Field_id,
		int	Ent_type,
		int	Ent_id,
		int	Pdeg
	)

----------------------------------------------------------- apr_set_ent_pdeg - to set the degree of approximation index associated with a given mesh entity ------------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success code, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity
	Pdeg	in: mesh entity ID in: degree of approximation

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int apr_set_ini_con	(	int	Field_id,
		double()(int, double , int)	Fun_p
	)

----------------------------------------------------------- apr_set_ini_con - to set an initial condition ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Fun_p	in: approximation field ID pointer to function that provides problem dependent initial condition data

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int apr_set_quadr_2D	(	int	Fa_type,
		int	Base_type,
		int *	Pdeg_vec,
		int *	Ngauss,
		double *	Xg,
		double *	Wg
	)

-------------------------------------------------------- apr_set_quadr_2D - to prepare quadrature data for a given face ---------------------------------------------------------

Parameters:

	Base_type	in: type of a face
	Pdeg_vec	in: type of basis functions: 1 (APC_TENSOR) - tensor product 2 (APC_COMPLETE) - complete polynomials
	Ngauss	in: element degree of polynomial
	Xg	out: number of gaussian points
	Wg	out: coordinates of gaussian points out: weights associated with points

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int apr_set_quadr_2D_penalty	(	int	Fa_type,
		int	Base_type,
		int *	Pdeg_vec,
		int *	Ngauss,
		double *	Xg,
		double *	Wg
	)

-------------------------------------------------------- apr_set_quadr_2D_penalty - to prepare penalty quadrature data for a given face ---------------------------------------------------------

Parameters:

	Base_type	in: type of a face
	Pdeg_vec	in: type of basis functions: (APC_TENSOR) - tensor product (APC_COMPLETE) - complete polynomials
	Ngauss	in: element degree of polynomial
	Xg	out: number of gaussian points
	Wg	out: coordinates of gaussian points out: weights associated with points

int apr_set_quadr_3D	(	int	Base_type,
		int *	Pdeg_vec,
		int *	Ngauss,
		double *	Xg,
		double *	Wg
	)

-------------------------------------------------------- apr_set_quadr_3D - to prepare quadrature data for a given element ---------------------------------------------------------

Parameters:

	Pdeg_vec	in: type of basis functions: 1 (APC_TENSOR) - tensor product 2 (APC_COMPLETE) - complete polynomials
	Ngauss	in: element degree of polynomial
	Xg	out: number of gaussian points
	Wg	out: coordinates of gaussian points out: weights associated with points

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int apr_shape_fun_3D	(	int	Base_type,
		int	Pdeg,
		double *	Eta,
		double *	Base_phi,
		double *	Base_dphix,
		double *	Base_dphiy,
		double *	Base_dphiz
	)

-------------------------------------------------------- apr_shape_fun_3D - to compute values of shape functions and their local derivatives at a point within the master 3D element ----------------------------------------------------------

Parameters:

	Base_type	returns: the number of shape functions (<=0 - failure)
	Pdeg	in: type of basis functions: REMARK: type of basis functions differentiates element types as well define APC_BASE_TENSOR_DG 1 - tensor product for prismatic elements and DG define APC_BASE_COMPLETE_DG 2 - complete polynomials for prismatic elements and DG define APC_BASE_PRISM_STD 3 // for linear prismatic elements define APC_BASE_TETRA_STD 4 // for linear tetrahedral elements
	Eta	in: degree of polynomial - can be either
	Base_phi	in: local coord of the considered point
	Base_dphix	out: basis functions
	Base_dphiy	out: x derivative of basis functions
	Base_dphiz	out: y derivative of basis functions out: z derivative of basis functions

int apr_sol_xglob	(	int	Field_id,
		double *	Xglob,
		int	Nb_sol,
		int *	El,
		double *	Xloc,
		double *	Sol,
		double *	Dxsol,
		double *	Dysol,
		double *	Dzsol,
		double	Close_proximity_precision,
		int	Sol_xglob_flags
	)

-------------------------------------------------------- apr_sol_xglob - to return the solution at a point with global coordinates specified. The procedure finds, for a given global point, the respective local coordinates within the proper initial mesh element, than computes corresponding local coordinates within an active ancestor of the initial element and finally finds the value of solution. There may be several initial mesh elements, several ancestors and several values due to the discontinuity of approximate solution. ---------------------------------------------------------

Parameters:

	Field_id	returns: >0 - success, <=0 - failure
	Xglob	in: field ID
	Nb_sol	in: global coordinates of a point
	El	in: which solution to take: 1 - sol_1, 2 - sol_2
	Xloc	out: list of element numbers, El[0] - number of elements on the list
	Sol	out: list of local coordinates within elements
	Dxsol	out: list of solutions at the point
	Dysol	out: list of derivatives wrt x of solution
	Dzsol	out: list of derivatives wrt y of solution
	Close_proximity_precision	out: list of derivatives wrt z of solution

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int apr_write_ent_dofs	(	int	Field_id,
		int	Ent_type,
		int	Ent_id,
		int	Ent_nrdofs,
		int	Vect_id,
		double *	Vect_dofs
	)

----------------------------------------------------------- apr_write_ent_dofs - to write a vector of dofs associated with a given mesh entity to approximation field data structure ------------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Ent_type	in: approximation field ID
	Ent_id	in: type of mesh entity
	Ent_nrdofs	in: mesh entity ID
	Vect_id	in: number of dofs associated with the entity
	Vect_dofs	in: vector ID in case of multiple solution vectors

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int apr_write_field	(	int	Field_id,
		int	Nreq,
		int	Select,
		double	Accuracy,
		char *	Filename
	)

-------------------------------------------------------- apr_write_field - to dump-out field data in the standard MOD_FEM format ---------------------------------------------------------

Parameters:

	Field_id	returns: >=0 - success code, <0 - error code
	Nreq	in: field ID
	Select	in: number of equations (scalar dofs)
	Accuracy	in: parameter to select written vectors
	Filename	in: parameter specyfying accuracy (put 0 for full accuracy in "%g" format) in: name of the file to write field data

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