The mapping from global to local degrees of freedom. More...
#include <Element.hh>
Inheritance diagram for pism::fem::Element:Public Member Functions | |
| ~Element ()=default | |
| int | n_chi () const |
| const Germ & | chi (unsigned int q, unsigned int k) const |
| int | n_pts () const |
| Number of quadrature points. More... | |
| double | weight (unsigned int q) const |
Weight of the quadrature point q More... | |
| template<typename T > | |
| void | evaluate (const T *x, T *result) const |
| Given nodal values, compute the values at quadrature points. More... | |
Protected Types | |
| typedef Germ(* | ShapeFunction) (unsigned int k, const QuadPoint &p) |
Protected Member Functions | |
| Element (const Grid &grid, int Nq, int n_chi, int block_size) | |
| Element (const DMDALocalInfo &grid_info, int Nq, int n_chi, int block_size) | |
| void | add_contribution (const double *K, Mat J) const |
| Add Jacobian contributions. More... | |
| void | mark_row_invalid (unsigned int k) |
Mark that the row corresponding to local degree of freedom k should not be updated when inserting into the global residual or Jacobian arrays. More... | |
| void | mark_col_invalid (unsigned int k) |
Mark that the column corresponding to local degree of freedom k should not be updated when inserting into the global Jacobian arrays. More... | |
| void | initialize (const double J[3][3], ShapeFunction f, unsigned int n_chi, const std::vector< QuadPoint > &points, const std::vector< double > &W) |
| Initialize shape function values and quadrature weights of a 2D physical element. More... | |
Protected Attributes | |
| DMDALocalInfo | m_grid |
| std::vector< int > | m_i_offset |
| std::vector< int > | m_j_offset |
| const unsigned int | m_n_chi |
| int | m_i |
| Indices of the current element. More... | |
| int | m_j |
| const unsigned int | m_Nq |
| Number of quadrature points. More... | |
| const int | m_block_size |
| std::vector< Germ > | m_germs |
| std::vector< MatStencil > | m_row |
| Stencils for updating entries of the Jacobian matrix. More... | |
| std::vector< MatStencil > | m_col |
| std::vector< double > | m_weights |
| Quadrature weights for a particular physical element. More... | |
Static Protected Attributes | |
| static const int | m_invalid_dof = -1073741824 |
Private Member Functions | |
| Element () | |
Detailed Description
The mapping from global to local degrees of freedom.
Computations of residual and Jacobian entries in the finite element method are done by iterating of the elements and adding the various contributions from each element. To do this, degrees of freedom from the global vector of unknowns must be remapped to element-local degrees of freedom for the purposes of local computation, (and the results added back again to the global residual and Jacobian arrays).
An Element mediates the transfer between element-local and global degrees of freedom and provides values of shape functions at quadrature points. In this implementation, the global degrees of freedom are either scalars (double's) or vectors (Vector2's), one per node in the Grid, and the local degrees of freedom on the element are q1::n_chi or p1::n_chi (i.e. four or three) scalars or vectors, one for each vertex of the element.
In addition to this, the Element transfers locally computed contributions to residual and Jacobian matrices to their global counterparts.
Definition at line 61 of file Element.hh.
The documentation for this class was generated from the following files:
- src/util/fem/Element.hh
- src/util/fem/Element.cc
