Flow123d
master-f44eb46
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#include <ref_element.hh>
Public Types | |
typedef arma::vec::fixed< dim > | LocalPoint |
typedef Armor::ArmaVec< double, dim+1 > | BaryPoint |
typedef Armor::ArmaVec< double, dim > | FaceBaryPoint |
typedef std::vector< BaryPoint > | BarycentricUnitVec |
typedef const std::vector< LocalPoint > & | CentersList |
Public Member Functions | |
DECLARE_EXCEPTION (ExcInvalidPermutation,<< "Side permutation not found.\n") | |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
vec::fixed< 1 > | normal_vector (unsigned int sid) |
vec::fixed< 2 > | normal_vector (unsigned int sid) |
vec::fixed< 3 > | normal_vector (unsigned int sid) |
auto | clip (const BaryPoint &barycentric) -> BaryPoint |
double | side_measure (unsigned int sid) |
double | side_measure (unsigned int sid) |
double | side_measure (unsigned int sid) |
unsigned int | line_between_faces (unsigned int f1, unsigned int f2) |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
template<unsigned int subdim> | |
auto | interpolate (arma::vec::fixed< subdim+1 > coord, int sub_simplex_idx) -> BaryPoint |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
unsigned int | count () |
template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim> | |
const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) > | interact (TInteraction< OutDim, InDim > interaction, bool inv) |
Static Public Member Functions | |
static LocalPoint | node_coords (unsigned int nid) |
static LocalPoint | normal_vector (unsigned int sid) |
static BaryPoint | clip (const BaryPoint &barycentric) |
static unsigned int | normal_orientation (unsigned int sid) |
static double | side_measure (unsigned int sid) |
static unsigned int | oposite_node (unsigned int sid) |
static unsigned int | line_between_faces (unsigned int f1, unsigned int f2) |
static BaryPoint | local_to_bary (const LocalPoint &lp) |
Converts from local to barycentric coordinates. More... | |
static LocalPoint | bary_to_local (const BaryPoint &bp) |
Converts from barycentric to local coordinates. More... | |
static BarycentricUnitVec | make_bary_unit_vec () |
static FaceBaryPoint | barycentric_on_face (const BaryPoint &barycentric, unsigned int i_face) |
static CentersList | centers_of_subelements (unsigned int sub_dim) |
static std::pair< unsigned int, unsigned int > | zeros_positions (const BaryPoint &barycentric, double tolerance=std::numeric_limits< double >::epsilon() *2) |
template<unsigned int subdim> | |
static unsigned int | topology_idx (unsigned int zeros_positions) |
template<unsigned int subdim> | |
static unsigned int | count () |
template<unsigned int subdim> | |
static arma::mat::fixed< dim+1, subdim+1 > | bary_coords (unsigned int sid) |
template<unsigned int subdim> | |
static BaryPoint | interpolate (arma::vec::fixed< subdim+1 > coord, int sub_simplex_idx) |
static BaryPoint | line_barycentric_interpolation (BaryPoint first_coords, BaryPoint second_coords, double first_theta, double second_theta, double theta) |
template<template< unsigned int OutDim, unsigned int InDim > class TInteraction, unsigned int OutDim, unsigned int InDim> | |
static const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) > | interact (TInteraction< OutDim, InDim > interaction, bool inv=false) |
Static Public Attributes | |
static const unsigned int | n_sides = dim + 1 |
Number of sides. More... | |
static const unsigned int | n_nodes = dim + 1 |
Number of nodes. More... | |
static const unsigned int | n_nodes_per_side = dim |
Number of nodes on one side. More... | |
static const unsigned int | n_lines_per_node = dim |
Number of lines with one common node. More... | |
static const unsigned int | n_nodes_per_line = 2 |
Number of nodes in one line. More... | |
static const unsigned int | n_sides_per_line = 2 |
Number of sides with one common line. dim == 3. More... | |
static const unsigned int | n_sides_per_node = dim |
Number of sides with one common line. More... | |
static const unsigned int | n_lines_per_side = (unsigned int)((dim * (dim - 1)) / 2) |
Number of lines on boundary of one side. More... | |
static const unsigned int | n_lines = (unsigned int)((dim * (dim + 1)) / 2) |
Number of lines, i.e. object of dimension dim-2 on the boundary of the reference element. More... | |
static const std::vector< std::vector< std::vector< unsigned int > > > | nodes_of_subelements |
Private Member Functions | |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 1 > > | node_lines_ |
const std::vector< IdxVector< 2 > > | node_lines_ |
const std::vector< IdxVector< 3 > > | side_nodes_ |
const std::vector< IdxVector< 3 > > | side_lines_ |
const IdxVector< 1 > | topology_zeros_ [] |
const IdxVector< 2 > | topology_zeros_ [] |
const IdxVector< 3 > | topology_zeros_ [] |
const IdxVector< 6 > | topology_zeros_ [] |
const IdxVector< 1 > | topology_zeros_ [] |
const IdxVector< 2 > | topology_zeros_ [] |
const IdxVector< 3 > | topology_zeros_ [] |
const IdxVector< 6 > | topology_zeros_ [] |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 2 > > | line_nodes_ |
const std::vector< IdxVector< 1 > > | node_lines_ |
const std::vector< IdxVector< 2 > > | node_lines_ |
const std::vector< IdxVector< 3 > > | node_lines_ |
const std::vector< IdxVector< 3 > > | side_nodes_ |
const std::vector< IdxVector< 3 > > | node_sides_ |
const std::vector< IdxVector< 2 > > | line_sides_ |
const std::vector< IdxVector< 3 > > | side_lines_ |
const IdxVector< 1 > | topology_zeros_ [] |
const IdxVector< 2 > | topology_zeros_ [] |
const IdxVector< 3 > | topology_zeros_ [] |
const IdxVector< 6 > | topology_zeros_ [] |
const IdxVector< 1 > | interact_ (unsigned int i, bool inv) |
This function is for "side_nodes" - for given side, give me nodes (0->0, 1->1). More... | |
const IdxVector< 2 > | interact_ (unsigned int i, bool inv) |
For line i {0}, give me indices of its nodes. More... | |
const IdxVector< 2 > | interact_ (unsigned int i, bool inv) |
For line i {0,1,2}, give me indices of its nodes. More... | |
const IdxVector< 2 > | interact_ (unsigned int i, bool inv) |
For line i {0,1,2,3,4,5}, give me indices of its nodes. More... | |
const IdxVector< 1 > | interact_ (unsigned int i, bool inv) |
For node i {0,1}, give me indices of lines. More... | |
const IdxVector< 2 > | interact_ (unsigned int i, bool inv) |
For node i {0,1,2}, give me indices of lines. More... | |
const IdxVector< 3 > | interact_ (unsigned int i, bool inv) |
For node i {0,1,2,3}, give me indices of lines. More... | |
const IdxVector< 3 > | interact_ (unsigned int i, bool inv) |
For side i {0,1,2}, give me indices of its nodes. More... | |
const IdxVector< 3 > | interact_ (unsigned int i, bool inv) |
For node i {0,1,2,3}, give me indices of sides. More... | |
const IdxVector< 2 > | interact_ (unsigned int i, bool inv) |
For line i {0,1,2,3}, give me indices of sides. More... | |
const IdxVector< 3 > | interact_ (unsigned int i, bool inv) |
For side i {0,1,2}, give me indices of its lines. More... | |
Static Private Member Functions | |
template<unsigned int OutDim, unsigned int InDim> | |
static const IdxVector<(InDim >OutDim ? InDim+1 :dim-InDim) > | interact_ (unsigned int index, bool inv=false) |
Internal part of the interact function. More... | |
Static Private Attributes | |
static const std::vector< IdxVector< n_nodes_per_line > > | line_nodes_ |
[n_lines] For given line, returns its nodes indices. More... | |
static const std::vector< IdxVector< n_lines_per_node > > | node_lines_ |
[n_nodes] For given node, returns lines indices. More... | |
static const std::vector< IdxVector< n_nodes_per_side > > | side_nodes_ |
[n_sides] For given side, returns nodes indices. For dim == 3. More... | |
static const std::vector< IdxVector< n_sides_per_node > > | node_sides_ |
[n_nodes] For given node, returns sides indices. For dim == 3. More... | |
static const std::vector< IdxVector< n_sides_per_line > > | line_sides_ |
[n_lines] For given line, returns sides indices. For dim == 3. More... | |
static const std::vector< IdxVector< n_lines_per_side > > | side_lines_ |
[n_sides] For given side, returns lines indices. For dim == 3. More... | |
static const IdxVector<(n_lines > n_nodes) ? n_lines :n_nodes > | topology_zeros_ [dim+1] |
Definition at line 339 of file ref_element.hh.
typedef std::vector<BaryPoint> RefElement< dim >::BarycentricUnitVec |
Definition at line 428 of file ref_element.hh.
typedef Armor::ArmaVec<double, dim+1> RefElement< dim >::BaryPoint |
Barycentric coordinates.
e.g. coordinates (a,b,c) on triangle with vertices X, Y, Z represents a point: a*X+b*Y+c*Z
Definition at line 349 of file ref_element.hh.
typedef const std::vector<LocalPoint>& RefElement< dim >::CentersList |
Definition at line 443 of file ref_element.hh.
typedef Armor::ArmaVec<double, dim> RefElement< dim >::FaceBaryPoint |
Definition at line 350 of file ref_element.hh.
typedef arma::vec::fixed<dim> RefElement< dim >::LocalPoint |
Definition at line 342 of file ref_element.hh.
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sid | - index of a sub-simplex in a simplex return an array of barycentric coordinates on <dim> simplex from <subdim> simplex for example: simplex<3> - ABCD and its subsubsimplex<1> AD (line index: 3) AD has barycoords for A (1,0), for D (0,1), but A in ABCD is (1,0,0,0) and D is (0,0,0,1) this method creates array ((1,0,0,0),(0,0,0,1)) |
Definition at line 604 of file ref_element.hh.
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Converts from barycentric to local coordinates.
bp | point in barycentric coordinates |
Definition at line 201 of file ref_element.cc.
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For given barycentric coordinates on the ref element returns barycentric coordinates on the ref. element of given face. Assumes that the input point is on the face. Barycentric order: (complanatory, local_coords )
Definition at line 279 of file ref_element.cc.
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Definition at line 366 of file ref_element.cc.
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If the given barycentric coordinate is in the ref. element, return unchanged. If the given barycentric coordinate is out of the ref. element, project it on the surface of the ref. element.
Definition at line 332 of file ref_element.cc.
auto RefElement< 0 >::clip | ( | const BaryPoint & | barycentric | ) | -> BaryPoint |
Definition at line 312 of file ref_element.cc.
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Function returns number of subdim-simplices inside dim-simplex. The aim is covering all the n_**** members with a single function. TODO: think of generalization for n_****_per_**** members, like function interact:
template<unsigned int subdimA, unsigned int subdimB> static unsigned int count();
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Definition at line 641 of file ref_element.hh.
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Definition at line 643 of file ref_element.hh.
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Definition at line 645 of file ref_element.hh.
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Definition at line 647 of file ref_element.hh.
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Definition at line 649 of file ref_element.hh.
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Definition at line 651 of file ref_element.hh.
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Definition at line 653 of file ref_element.hh.
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Definition at line 655 of file ref_element.hh.
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Definition at line 657 of file ref_element.hh.
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Definition at line 659 of file ref_element.hh.
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Definition at line 661 of file ref_element.hh.
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Definition at line 663 of file ref_element.hh.
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Definition at line 665 of file ref_element.hh.
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Definition at line 667 of file ref_element.hh.
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Definition at line 669 of file ref_element.hh.
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Definition at line 671 of file ref_element.hh.
RefElement< dim >::DECLARE_EXCEPTION | ( | ExcInvalidPermutation | , |
<< "Side permutation not found.\n" | |||
) |
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Definition at line 753 of file ref_element.hh.
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Usage: RefElement<3>::interact(Interaction<2,0>(1)) (means: In tetrahedron <3>, give indices of sides <2>, connected by node <0> with index 1) RefElement<3>::interact(Interaction<2,0>(1))[1] (as above, but give only the side with index 1)
Template usage: RefElement<dim>::interact(Interaction<OutDim, InDim>(i))[j] (means: on dim-dimensional reference element, go on InDim-dimensional subelement with index i, which connects OutDim-dimnesional subelements and select the one with index j)
This method serves as an interface to topology information of the reference element. It returns indices of OutDim-dimensional object of InDim-dimnesional object of given index in dim-dimnesional reference element.
interaction | - auxilliary object carying the index and the template arguments OutDim and InDim |
OutDim | - output dimension (give me node-0, line-1, side-2), <= dim |
InDim | - input dimension (for node-0, line-1, side-2), <= dim |
IdxVector
object.possible calls: dim OutDim InDim return 1,2,3 0 1 InDim+1 - give me indices of nodes of line of given index 3 0 2 InDim+1 - give me indices of nodes of a side (triangle) of given index 3 1 2 InDim+1 - give me indices of lines of side (triangle) of given index
1,2,3 1 0 dim-InDim - give me indices of lines with common node of given index 3 2 0 dim-InDim - give me indices of sides (triangles) with common node of given index 3 2 1 dim-InDim - give me indices of sides (triangles) with common line of given index
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This function is for "side_nodes" - for given side, give me nodes (0->0, 1->1).
Definition at line 687 of file ref_element.hh.
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For line i {0}, give me indices of its nodes.
Definition at line 692 of file ref_element.hh.
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For line i {0,1,2}, give me indices of its nodes.
Definition at line 697 of file ref_element.hh.
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For line i {0,1,2,3,4,5}, give me indices of its nodes.
Definition at line 702 of file ref_element.hh.
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For node i {0,1}, give me indices of lines.
Definition at line 707 of file ref_element.hh.
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For node i {0,1,2}, give me indices of lines.
Definition at line 712 of file ref_element.hh.
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For node i {0,1,2,3}, give me indices of lines.
Definition at line 717 of file ref_element.hh.
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For side i {0,1,2}, give me indices of its nodes.
Definition at line 722 of file ref_element.hh.
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For node i {0,1,2,3}, give me indices of sides.
Definition at line 727 of file ref_element.hh.
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For line i {0,1,2,3}, give me indices of sides.
Definition at line 732 of file ref_element.hh.
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For side i {0,1,2}, give me indices of its lines.
Definition at line 737 of file ref_element.hh.
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Internal part of the interact function.
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Interpolate barycentric coords to a higher dimension of a simplex.
coord | - barycentric coords of a point on a sub-simplex |
sub_simplex_idx | - id of sub-simplex on a simplex |
auto RefElement< dim >::interpolate | ( | arma::vec::fixed< subdim+1 > | coord, |
int | sub_simplex_idx | ||
) | -> BaryPoint |
Definition at line 635 of file ref_element.hh.
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Basic line interpolation.
Basic line interpolation
Definition at line 437 of file ref_element.cc.
unsigned int RefElement< 3 >::line_between_faces | ( | unsigned int | f1, |
unsigned int | f2 | ||
) |
Definition at line 423 of file ref_element.cc.
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Return index of 1D line, shared by two faces f1
and f2
of the reference tetrahedron. Implemented only for dim
== 3.
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Definition at line 45 of file ref_element.cc.
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Definition at line 48 of file ref_element.cc.
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Definition at line 53 of file ref_element.cc.
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Definition at line 560 of file ref_element.hh.
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Definition at line 561 of file ref_element.hh.
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Definition at line 562 of file ref_element.hh.
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Definition at line 569 of file ref_element.hh.
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Converts from local to barycentric coordinates.
lp | point in local coordinates (x,y) |
Definition at line 187 of file ref_element.cc.
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Used in the clip method.
Definition at line 318 of file ref_element.cc.
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Return coordinates of given node.
RefElement
nid | Node number. NOTE: Implementation is dependent on current node and side numbering. |
Definition at line 619 of file ref_element.hh.
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Definition at line 62 of file ref_element.cc.
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Definition at line 66 of file ref_element.cc.
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Definition at line 563 of file ref_element.hh.
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Definition at line 564 of file ref_element.hh.
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Definition at line 566 of file ref_element.hh.
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Definition at line 568 of file ref_element.hh.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 0 >::nodes_of_subelements |
Definition at line 163 of file ref_element.cc.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 1 >::nodes_of_subelements |
Definition at line 167 of file ref_element.cc.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 2 >::nodes_of_subelements |
Definition at line 172 of file ref_element.cc.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 3 >::nodes_of_subelements |
Definition at line 178 of file ref_element.cc.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 0 >::nodes_of_subelements |
Definition at line 587 of file ref_element.hh.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 1 >::nodes_of_subelements |
Definition at line 588 of file ref_element.hh.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 2 >::nodes_of_subelements |
Definition at line 589 of file ref_element.hh.
const std::vector< std::vector< std::vector< unsigned int > > > RefElement< 3 >::nodes_of_subelements |
Definition at line 590 of file ref_element.hh.
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Returns orientation of the normal of side sid
. 0 -> OUT, 1 -> IN. NOTE: Implementation is dependent on current node and side numbering.
Definition at line 216 of file ref_element.cc.
vec::fixed< 1 > RefElement< 1 >::normal_vector | ( | unsigned int | sid | ) |
Definition at line 225 of file ref_element.cc.
vec::fixed< 2 > RefElement< 2 >::normal_vector | ( | unsigned int | sid | ) |
Definition at line 233 of file ref_element.cc.
vec::fixed< 3 > RefElement< 3 >::normal_vector | ( | unsigned int | sid | ) |
Definition at line 255 of file ref_element.cc.
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Compute normal vector to a given side.
sid | Side number. |
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Returns index of the node that is oposite to side of given index sid
. Note: It is dependent on current node and side numbering.
sid | Side number. NOTE: Implementation is dependent on current node and side numbering. |
Definition at line 209 of file ref_element.cc.
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Definition at line 97 of file ref_element.cc.
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Definition at line 570 of file ref_element.hh.
double RefElement< 1 >::side_measure | ( | unsigned int | sid | ) |
Definition at line 394 of file ref_element.cc.
double RefElement< 2 >::side_measure | ( | unsigned int | sid | ) |
Definition at line 403 of file ref_element.cc.
double RefElement< 3 >::side_measure | ( | unsigned int | sid | ) |
Definition at line 412 of file ref_element.cc.
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Definition at line 76 of file ref_element.cc.
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Definition at line 567 of file ref_element.hh.
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According to positions of zeros in barycentric coordinates, it gives the index of subdim-simplex in the reference element. Number of zeros must be equal to (3-subdim). e.g.: if 1 zeros, return index of side (subdim 2) if 2 zeros, return index of edge (subdim 1) if 3 zeros, return index of vertex (subdim 0)
Definition at line 676 of file ref_element.hh.
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Definition at line 104 of file ref_element.cc.
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Definition at line 109 of file ref_element.cc.
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Definition at line 117 of file ref_element.cc.
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Definition at line 129 of file ref_element.cc.
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Definition at line 554 of file ref_element.hh.
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Definition at line 555 of file ref_element.hh.
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Definition at line 556 of file ref_element.hh.
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Definition at line 557 of file ref_element.hh.
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Definition at line 573 of file ref_element.hh.
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Definition at line 574 of file ref_element.hh.
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Definition at line 575 of file ref_element.hh.
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Definition at line 576 of file ref_element.hh.
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Return (1) number of zeros and (2) positions of zeros in barycentric coordinates. tolerance
serves for testing zero values of barycentric
coordinates.
Definition at line 294 of file ref_element.cc.
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[n_lines] For given line, returns its nodes indices.
Definition at line 533 of file ref_element.hh.
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[n_lines] For given line, returns sides indices. For dim
== 3.
Definition at line 537 of file ref_element.hh.
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Number of lines, i.e. object
of dimension dim-2
on the boundary of the reference element.
Definition at line 410 of file ref_element.hh.
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Number of lines with one common node.
Definition at line 401 of file ref_element.hh.
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Number of lines on boundary of one side.
Definition at line 407 of file ref_element.hh.
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Number of nodes.
Definition at line 399 of file ref_element.hh.
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Number of nodes in one line.
Definition at line 402 of file ref_element.hh.
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Number of nodes on one side.
Definition at line 400 of file ref_element.hh.
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Number of sides.
Definition at line 398 of file ref_element.hh.
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Number of sides with one common line. dim
== 3.
Definition at line 403 of file ref_element.hh.
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Number of sides with one common line.
Definition at line 404 of file ref_element.hh.
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[n_nodes] For given node, returns lines indices.
Definition at line 534 of file ref_element.hh.
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[n_nodes] For given node, returns sides indices. For dim
== 3.
Definition at line 536 of file ref_element.hh.
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Definition at line 413 of file ref_element.hh.
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[n_sides] For given side, returns lines indices. For dim
== 3.
Definition at line 538 of file ref_element.hh.
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[n_sides] For given side, returns nodes indices. For dim
== 3.
Definition at line 535 of file ref_element.hh.
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Consider an n-face (node, edge, face, bulk) with dimension subdim
and index within subdimension idx
. Barycentric coordinates of all points on the n-face have unique pattern of zero coordinates.
topology_zeros_[subdim][idx] is a bitfield with '1' where the pattern have zeros.
Definition at line 548 of file ref_element.hh.