geo(3)

NAME

geo - the finite element mesh class

SYNOPSYS

The geo class defines a container for a finite element mesh. This describes the nodes coordinates and the connectivity. geo can contains domains, usefull for boundary condition setting.

EXAMPLE

A sample usage of the geo class writes

#include "rheolef/rheolef.h"
void main () {

geo g;
cin >> g;
cout << plotmtv << g;

}

DESCRIPTION

The empty constructor makes an empty geo. A string argument, as

geo g("square");

will recursively look for a `square.geo[.gz]' file in the directory mentionned by the RHEOPATH environment variable, while gzip decompression is assumed. If the file starts with `.' as `./square' or with a `/' as in `/home/oscar/square', no search occurs. Also, if the environment variable RHEOPATH is not set, the default value is the current directory.

Input and output on streams are available, and manipulators works for text or graphic output (see geo(1)).

Finally, an STL-like interface provides efficient accesses to nodes, elements and domains.

MESH ADAPTATION

The geo_adapt functions performs a mesh adaptation to improve the P1-Lagrange interpolation of the field given in argument (see field(3)).

AXISYMETRIC GEOMETRY

The coordinate_system and set_coordinate_system members supports both cartesian, rz and zr (axisymmetric) coordinate systems. This information is used by the form class (see form(3)).

ACCESS TO CONNECTIVITY

The folowing code prints triangle vertex numbers

geo omega ("circle");
for (geo::const_iterator i = g.begin(); i != i.end(); i++) {

const geo_element& K = *i;
if (K.name() != 't') continue;
for (geo::size_type j = 0; j < 3; j++)

cout << K [j] << " ";

cout << endl;

}

See . geo_element internal}'.

ACCESS TO VERTICE COORDINATES

The folowing code prints vertices coordinate

for (geo::const_iterator_vertex i = g.begin_vertex(); i != g.end_node(); i++) {

const point& xi = *i;
for (geo::size_type j = 0; j < g.dimension(); j++)

cout << xi [j] << " ";

cout << endl;

}

ACCESS TO DOMAINS

The following code prints edges on domain:

for (geo::const_iterator_domain i = g.begin_domain(); i != i.end_domain(); i++) {

const domain& dom = *i;
if (dom.dimension() != 2) continue;
for (domain::const_iterator j = dom.begin(); j < dom.end(); j++) {

const geo_element& E = *j;
cout << E [0] << " " << E[1] << endl;

}
cout << endl;

}

See domain(3).

ENVIRONS

RHEOPATH: search path for geo data file. Also form(3).

IMPLEMENTATION

class geo : public smart_pointer<georep> {
public:

// typedefs:

typedef georep::plot_options plot_options;
void write_gnuplot_postscript_options (std::ostream& plot, const plot_options& opt) const;

typedef georep::iterator iterator;
typedef georep::const_iterator const_iterator;
typedef georep::elemlist_type elemlist_type;
typedef georep::nodelist_type nodelist_type;
typedef georep::size_type size_type;
typedef georep::domlist_type domlist_type;

typedef georep::const_iterator_node const_iterator_node;
typedef georep::const_iterator_vertex const_iterator_vertex;
typedef georep::const_iterator_domain const_iterator_domain;
typedef georep::iterator_node iterator_node;
typedef georep::iterator_vertex iterator_vertex;
typedef georep::iterator_domain iterator_domain;

// allocators/deallocators:

explicit geo (const std::string& filename, const std::string& coord_sys = "cartesian");
geo(const geo& g, const domain& d);
geo(const nodelist_type& p, const geo& g);
geo();

friend geo geo_adapt (const class field& criteria, const Float& hcoef,

bool reinterpolate_criteria = false);

friend geo geo_adapt (const class field& criteria,

const adapt_option_type& = adapt_option_type(),
bool reinterpolate_criteria = false);

friend geo geo_metric_adapt (const field& mh,

const adapt_option_type& = adapt_option_type());

// input/output:

friend std::istream& operator >> (std::istream&, geo&);
friend std::ostream& operator << (std::ostream&, const geo&);
void save () const;
void use_double_precision_in_saving();
std::ostream& dump (std::ostream& s = std::cerr) const;
std::ostream& put_mtv_domains (std::ostream&, size_type=0) const;

// accessors:

const point& vertex (size_type i) const;
const geo_element& element (size_type K_idx) const;
Float measure (const geo_element& K) const;

std::string name() const;
std::string basename() const;
// Family name plus number
std::string familyname() const;
// For moving boundary problems
size_type number() const;
// Number of moving boundary mesh
size_type version() const;
// Refinment iteration for the current mesh number
size_type dimension() const;
size_type map_dimension() const;
std::string coordinate_system () const; // "cartesian", "rz", "zr"
fem_helper::coordinate_type coordinate_system_type() const;

size_type serial_number() const;

const domain& boundary() const;
void build_subregion(const domain& start_from, const domain& dont_cross,

std::string name, std::string name_of_complement="");

// Builds a new domain on the side of domain `dont_cross' on which `start_from' // lies. These must have no intersection.

size_type size() const;
size_type n_element() const; // same as size()
size_type n_vertex() const;
size_type n_vertice() const;
size_type n_node() const; // same as n_vertex()
size_type n_edge() const ;
size_type n_face() const ;
size_type n_triangle() const ;
size_type n_quadrangle() const ;
size_type n_volume() const ;
size_type n_tetraedra() const ;
size_type n_prism() const ;
size_type n_hexaedra() const ;
size_type n_subgeo(size_type d) const ;
size_type n_element(reference_element::enum_type t) const;

Float hmin() const;
Float hmax() const;
const point& xmin() const;
const point& xmax() const;

meshpoint hatter (const point& x, size_type K) const;
point dehatter (const meshpoint& S) const;
point dehatter (const point& x_hat, size_type e) const;

const_iterator begin() const;
const_iterator end() const;
const_iterator_node begin_node() const;
const_iterator_node end_node() const;
const_iterator_vertex begin_vertex() const;
const_iterator_vertex end_vertex() const;

// localizer:
bool localize (const point& x, geo_element::size_type& element) const;
void localize_nearest (const point& x, point& y, geo_element::size_type& element) const;
bool trace (const point& x0, const point& v, point& x, Float& t, size_type& element) const;

// access to domains:
const domain& get_domain(size_type i) const;
size_type n_domain() const;
bool has_domain (const std::string& domname) const;
const domain& operator[] (const std::string& domname) const;
const_iterator_domain begin_domain() const;
const_iterator_domain end_domain() const;

point normal (const geo_element& S) const;
point normal (const geo_element& K, georep::size_type side_idx) const;
void
sort_interface(const domain&, const interface&) const;
class field
normal (const class space& Nh, const domain& d,

const std::string& region="") const;

class field
normal (const class space& Nh, const domain& d, const interface& bc) const;
class field
tangent (const class space& Nh, const domain& d,

const std::string& region="") const;

class field
tangent (const class space& Nh, const domain& d, const interface& bc) const;

// Gives normal to d in discontinuous space Nh (P0 or P1d) and can // initialize orientation of domain through `bc' data structure.
// Currently limited to straight-sided elements.

class field
tangent_spline (const space& Nh, const domain& d, const interface& bc) const;
class field
plane_curvature (const space& Nh, const domain& d,

const interface& bc) const;

// Gives curvature of d in the (x,y) or (r,z) plane.
// Currently limited to straight-sided elements.

class field
plane_curvature_spline (const space& Nh, const domain& d,

const interface& bc) const;

// Gives curvature of d in the (x,y) or (r,z) plane based on a spline interpolation.

class field
plane_curvature_quadratic (const space& Nh, const domain& d,

const interface& bc) const;

// Gives curvature of d in the (x,y) or (r,z) plane based on a local quadratic interpolation.

class field
axisymmetric_curvature (const class space& Nh, const domain& d) const;
class field
axisymmetric_curvature (const class space& Nh, const domain& d,

const interface& bc) const;

// Specific to "rz" and "zr" coordinate systems:
// Gives curvature of d in a plane orthogonal to the (r,z) plane.
// Can also initialize orientation of domain through `bc' data structure. // Currently limited to straight-sided elements.

void
interface_process (const domain& d, const interface& bc,

geometric_event& event) const;

// Detects event along domain d sorted according to bc's.

// construction of jump-interface domain data:
void jump_interface(const domain& interface, const domain& subgeo,

std::map<size_type, tiny_vector<size_type> >& special_elements, std::map<size_type,size_type>& node_global_to_interface) const;

// comparator:

bool operator == (const geo&) const;
bool operator != (const geo&) const;

// modifiers

void set_name (const std::string&);
void set_coordinate_system (const std::string&); // "cartesian", "rz", "zr" void upgrade();
void label_interface(const domain& dom1, const domain& dom2, const std::string& name);

// modify domains
void erase_domain (const std::string& name);
void insert_domain (const domain&);

// accessors to internals:

bool localizer_initialized () const;
void init_localizer (const domain& boundary, Float tolerance=-1, int list_size=0) const;
const size_type* get_geo_counter() const;
const size_type* get_element_counter() const;

// TO BE REMOVED
int gnuplot2d (const std::string& basename,

plot_options& opt) const;

// check consistency

void check() const;

protected:

friend class spacerep;
friend class field;

void may_have_version_2() const; // fatal if not !

// modifiers to internals:

void set_dimension (size_type d);
iterator begin();
iterator end();
iterator_node begin_node();
iterator_node end_node();
iterator_vertex begin_vertex();
iterator_vertex end_vertex();

};

SEE ALSO

geo(1), field(3), form(3), domain(3), form(3)

rheolef-5.89 geo(3)