/usr/include/deal.II/fe/fe_poly_tensor.h is in libdeal.ii-dev 6.3.1-1.1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 | //---------------------------------------------------------------------------
// $Id: fe_poly_tensor.h 18933 2009-06-12 08:53:35Z bangerth $
// Version: $Name$
//
// Copyright (C) 2005, 2006, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__fe_poly_tensor_h
#define __deal2__fe_poly_tensor_h
#include <lac/full_matrix.h>
#include <fe/fe.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup febase */
/*@{*/
/**
* This class gives a unified framework for the implementation of
* FiniteElement classes based on Tensor valued polynomial spaces like
* PolynomialsBDM and PolynomialsRaviartThomas.
*
* Every class that implements following function can be used as
* template parameter POLY.
*
* @code
* void compute (const Point<dim> &unit_point,
* std::vector<Tensor<1,dim> > &values,
* std::vector<Tensor<2,dim> > &grads,
* std::vector<Tensor<3,dim> > &grad_grads) const;
* @endcode
*
* In many cases, the node functionals depend on the shape of the mesh
* cell, since they evaluate normal or tangential components on the
* faces. In order to allow for a set of transformations, the variable
* #mapping_type has been introduced. It should also be set in the
* constructor of a derived class.
*
* This class is not a fully implemented FiniteElement class, but
* implements some common features of vector valued elements based on
* vector valued polynomial classes. What's missing here in particular
* is information on the topological location of the node values.
*
* For more information on the template parameter <tt>spacedim</tt>,
* see the documentation for the class Triangulation.
*
* <h3>Deriving classes</h3>
*
* Any derived class must decide on the polynomial space to use. This
* polynomial space should be implemented simply as a set of vector
* valued polynomials like PolynomialsBDM and
* PolynomialsRaviartThomas. In order to facilitate this
* implementation, the basis of this space may be arbitrary.
*
* <h4>Determining the correct basis</h4>
*
* In most cases, the set of desired node values $N_i$ and the basis
* functions $v_j$ will not fulfill the interpolation condition
* $N_i(v_j) = \delta_{ij}$.
*
* The use of the member data #inverse_node_matrix allows to compute
* the basis $v_j$ automatically, after the node values
* for each original basis function of the polynomial space have been
* computed.
*
* Therefore, the constructor of a derived class should have a
* structure like this (example for interpolation in support points):
*
* @verbatim
* fill_support_points();
*
* const unsigned int n_dofs = this->dofs_per_cell;
* FullMatrix<double> N(n_dofs, n_dofs);
*
* for (unsigned int i=0;i<n_dofs;++i)
* {
* const Point<dim>& p = this->unit_support_point[i];
*
* for (unsigned int j=0;j<n_dofs;++j)
* for (unsigned int d=0;d<dim;++d)
* N(i,j) += node_vector[i][d]
* * this->shape_value_component(j, p, d);
* }
*
* this->inverse_node_matrix.reinit(n_dofs, n_dofs);
* this->inverse_node_matrix.invert(N);
* @endverbatim
*
* @note The matrix #inverse_node_matrix should have dimensions zero
* before this piece of code is executed. Only then,
* shape_value_component() will return the raw bolynomial <i>j</i> as
* defined in the polynomial space POLY.
*
* <h4>Setting the transformation</h4>
*
* In most cases, vector valued basis functions must be transformed
* when mapped from the reference cell to the actual grid cell. These
* transformations can be selected from the set MappingType and stored
* in #mapping_type. Therefore, each constructor should contain a line
* like:
* @verbatim
* this->mapping_type = this->mapping_none;
* @endverbatim
*
* @see PolynomialsBDM, PolynomialsRaviartThomas
*
* @author Guido Kanschat, 2005
**/
template <class POLY, int dim, int spacedim=dim>
class FE_PolyTensor : public FiniteElement<dim,spacedim>
{
public:
/**
* Constructor.
*
* @arg @c degree: constructor
* argument for poly. May be
* different from @p
* fe_data.degree.
*/
FE_PolyTensor (const unsigned int degree,
const FiniteElementData<dim> &fe_data,
const std::vector<bool> &restriction_is_additive_flags,
const std::vector<std::vector<bool> > &nonzero_components);
/**
* Since these elements are
* vector valued, an exception is
* thrown.
*/
virtual double shape_value (const unsigned int i,
const Point<dim> &p) const;
virtual double shape_value_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Since these elements are
* vector valued, an exception is
* thrown.
*/
virtual Tensor<1,dim> shape_grad (const unsigned int i,
const Point<dim> &p) const;
virtual Tensor<1,dim> shape_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Since these elements are
* vector valued, an exception is
* thrown.
*/
virtual Tensor<2,dim> shape_grad_grad (const unsigned int i,
const Point<dim> &p) const;
virtual Tensor<2,dim> shape_grad_grad_component (const unsigned int i,
const Point<dim> &p,
const unsigned int component) const;
/**
* Number of base elements in a
* mixed discretization. Since
* this is not a composed element,
* return one.
*/
virtual unsigned int n_base_elements () const;
/**
* Access to base element
* objects. Since this element is
* not composed of several elements,
* <tt>base_element(0)</tt> is
* <tt>this</tt>, and all other
* indices throw an error.
*/
virtual const FiniteElement<dim,spacedim> &
base_element (const unsigned int index) const;
/**
* Multiplicity of base element
* <tt>index</tt>. Since this is
* not a composed element,
* <tt>element_multiplicity(0)</tt>
* returns one, and all other
* indices will throw an error.
*/
virtual unsigned int element_multiplicity (const unsigned int index) const;
/**
* Given <tt>flags</tt>,
* determines the values which
* must be computed only for the
* reference cell. Make sure,
* that #mapping_type is set by
* the derived class, such that
* this function can operate
* correctly.
*/
virtual UpdateFlags update_once (const UpdateFlags flags) const;
/**
* Given <tt>flags</tt>,
* determines the values which
* must be computed in each cell
* cell. Make sure, that
* #mapping_type is set by the
* derived class, such that this
* function can operate
* correctly.
*/
virtual UpdateFlags update_each (const UpdateFlags flags) const;
protected:
/**
* The mapping type to be used to
* map shape functions from the
* reference cell to the mesh
* cell.
*/
MappingType mapping_type;
virtual
typename Mapping<dim,spacedim>::InternalDataBase *
get_data (const UpdateFlags,
const Mapping<dim,spacedim>& mapping,
const Quadrature<dim>& quadrature) const ;
virtual void
fill_fe_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const Quadrature<dim> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim> &data,
CellSimilarity::Similarity &cell_similarity) const;
virtual void
fill_fe_face_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim>& data) const ;
virtual void
fill_fe_subface_values (const Mapping<dim,spacedim> &mapping,
const typename Triangulation<dim,spacedim>::cell_iterator &cell,
const unsigned int face_no,
const unsigned int sub_no,
const Quadrature<dim-1> &quadrature,
typename Mapping<dim,spacedim>::InternalDataBase &mapping_internal,
typename Mapping<dim,spacedim>::InternalDataBase &fe_internal,
FEValuesData<dim,spacedim>& data) const ;
/**
* Fields of cell-independent
* data for FE_PolyTensor. Stores
* the values of the shape
* functions and their
* derivatives on the reference
* cell for later use.
*
* All tables are organized in a
* way, that the value for shape
* function <i>i</i> at
* quadrature point <i>k</i> is
* accessed by indices
* <i>(i,k)</i>.
*/
class InternalData : public FiniteElement<dim,spacedim>::InternalDataBase
{
public:
/**
* Array with shape function
* values in quadrature
* points. There is one
* row for each shape
* function, containing
* values for each quadrature
* point.
*/
std::vector<std::vector<Tensor<1,dim> > > shape_values;
/**
* Array with shape function
* gradients in quadrature
* points. There is one
* row for each shape
* function, containing
* values for each quadrature
* point.
*/
std::vector<std::vector<Tensor<2,dim> > > shape_grads;
};
/**
* The polynomial space. Its type
* is given by the template
* parameter POLY.
*/
POLY poly_space;
/**
* The inverse of the matrix
* <i>a<sub>ij</sub></i> of node
* values <i>N<sub>i</sub></i>
* applied to polynomial
* <i>p<sub>j</sub></i>. This
* matrix is used to convert
* polynomials in the "raw" basis
* provided in #poly_space to the
* basis dual to the node
* functionals on the reference cell.
*
* This object is not filled by
* FE_PolyTensor, but is a chance
* for a derived class to allow
* for reorganization of the
* basis functions. If it is left
* empty, the basis in
* #poly_space is used.
*/
FullMatrix<double> inverse_node_matrix;
/**
* If a shape function is
* computed at a single point, we
* must compute all of them to
* apply #inverse_node_matrix. In
* order to avoid too much
* overhead, we cache the point
* and the function values for
* the next evaluation.
*/
mutable Point<dim> cached_point;
/**
* Cached shape function values after
* call to
* shape_value_component().
*/
mutable std::vector<Tensor<1,dim> > cached_values;
/**
* Cached shape function gradients after
* call to
* shape_grad_component().
*/
mutable std::vector<Tensor<2,dim> > cached_grads;
/**
* Cached second derivatives of
* shape functions after call to
* shape_grad_grad_component().
*/
mutable std::vector<Tensor<3,dim> > cached_grad_grads;
};
/*@}*/
DEAL_II_NAMESPACE_CLOSE
#endif
|