NAME
space - piecewise polynomial finite element space (rheolef-7.2)
DESCRIPTION
The space class contains the numbering of the degrees of freedoms. The degrees of freedoms are the coefficients in the basis of the vectorial space of piecewise polynomial finite element functions. The set of degrees of freedom coefficients is splited in two subsets: the unknowns and the blocked degrees of freedoms. The blocked degrees of freedom are associated to Dirichlet boundary conditions, where the values of the function, and thus, of the coefficients, are prescribed. The unknown degrees of freedom are all the others. Finally, the space class is mainly a table of renumbering for these coefficients.
The space is characterized by two entities: its finite element, described by the basis(2) class and its mesh, described by the geo(2) class. By default, the space is scalar valued. It extends to vector and tensor valued functions.
EXAMPLE
space Q (omega,
’P1’);
space V (omega, ’P2’, ’vector’);
space T (omega, ’P1d’,
’tensor’);
PRODUCT OF SPACES
space X =
T*V*Q;
space Q2 = pow(Q,2);
SPACE OF REALS
The ’space::real()’ function returns the space of reals and could be used in a product of spaces as:
space IR =
space::real();
space Yh = Xh*IR;
This convention is useful e.g. when a Lagrange multiplier is a real, not a field. It extends to IR^n for any size_t n as:
space IRn = pow(IR,n);
IMPLEMENTATION
This documentation has been generated from file main/lib/space.h
The space class is simply an alias to the space_basic class
typedef space_basic<Float> space;
The space_basic class provides an interface to a data container:
template
<class T>
class space_basic<T,sequential> : public
smart_pointer<space_rep<T,sequential> > {
public:
// typedefs:
typedef
space_rep<T,sequential> rep;
typedef smart_pointer<rep> base;
typedef typename rep::size_type size_type;
typedef typename rep::valued_type valued_type;
// allocators:
space_basic
(const geo_basic<T,sequential>& omega =
(geo_basic<T,sequential>()),
std::string approx = "",
std::string prod_valued = "scalar");
space_basic (const geo_basic<T,sequential>& omega,
const basis_basic<T>& b);
space_basic (const space_mult_list<T,sequential>&
expr);
space_basic (const
space_constitution<T,sequential>& constit);
static space_basic<T,sequential> real();
// accessors:
void block
(std::string dom_name);
void unblock(std::string dom_name);
void block (const
domain_indirect_basic<sequential>& dom);
void unblock(const
domain_indirect_basic<sequential>& dom);
void block_n
(std::string dom_name);
void unblock_n(std::string dom_name);
void block_n (const
domain_indirect_basic<sequential>& dom);
void unblock_n(const
domain_indirect_basic<sequential>& dom);
const
distributor& ownership() const;
const communicator& comm() const;
size_type ndof() const;
size_type dis_ndof() const;
const
geo_basic<T,sequential>& get_geo() const;
const basis_basic<T>& get_basis() const;
size_type size() const;
valued_type valued_tag() const;
const std::string& valued() const;
space_component<T,sequential> operator[] (size_type
i_comp);
space_component_const<T,sequential> operator[]
(size_type i_comp) const;
const space_constitution<T,sequential>&
get_constitution() const;
size_type degree() const;
std::string get_approx() const;
std::string name() const;
void dis_idof (const geo_element& K, std::vector<size_type>& dis_idof) const;
const
distributor& iu_ownership() const;
const distributor& ib_ownership() const;
bool is_blocked
(size_type idof) const;
size_type dis_iub (size_type idof) const;
bool dis_is_blocked (size_type dis_idof) const;
size_type dis_idof2dis_iub (size_type dis_idof) const;
const
distributor& ios_ownership() const;
size_type idof2ios_dis_idof (size_type idof) const;
size_type ios_idof2dis_idof (size_type ios_idof) const;
const
point_basic<T>& xdof (size_type idof) const;
const disarray<point_basic<T>,sequential>&
get_xdofs() const;
template
<class Function>
T momentum (const Function& f, size_type idof)
const;
template
<class Function>
point_basic<T> vector_momentum (const Function& f,
size_type idof) const;
template
<class Function>
tensor_basic<T> tensor_momentum (const Function&
f, size_type idof) const;
disarray<size_type,
sequential> build_dom_dis_idof2bgd_dis_idof (
const space_basic<T,sequential>& Wh, const
std::string& dom_name) const;
disarray<size_type,
sequential> build_dom_dis_idof2bgd_dis_idof (
const space_basic<T,sequential>& Wh, const
geo_basic<T,sequential>& bgd_gamma) const;
const
std::set<size_type>& ext_iu_set() const { return
base::data().ext_iu_set(); }
const std::set<size_type>& ext_ib_set() const {
return base::data().ext_ib_set(); }
// comparator:
bool operator==
(const space_basic<T,sequential>& V2) const {
return base::data().operator==(V2.data()); }
bool operator!= (const space_basic<T,sequential>&
V2) const { return ! operator== (V2); }
friend bool are_compatible (const
space_basic<T,sequential>& V1, const
space_basic<T,sequential>& V2) {
return are_compatible (V1.data(), V2.data()); }
// for lazy (un-assembled) on geo_domains:
template
<class Set>
void get_parent_subgeo_owner_dis_indexes (Set&
ext_dis_idofs) const
{ base::data().get_parent_subgeo_owner_dis_indexes
(ext_dis_idofs); }
size_type get_parent_subgeo_owner (size_type dis_idof) const
{ return base::data().get_parent_subgeo_owner (dis_idof); }
};
AUTHOR
Pierre Saramito <Pierre.Saramito [AT] imag.fr>
COPYRIGHT
Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito [AT] imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>;. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.