/usr/include/deal.II/matrix_free/shape_info.templates.h is in libdeal.ii-dev 8.4.2-2+b1.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 | // ---------------------------------------------------------------------
//
// Copyright (C) 2011 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#include <deal.II/base/utilities.h>
#include <deal.II/base/memory_consumption.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/polynomials_piecewise.h>
#include <deal.II/fe/fe_poly.h>
#include <deal.II/fe/fe_dgp.h>
#include <deal.II/fe/fe_q_dg0.h>
#include <deal.II/matrix_free/shape_info.h>
DEAL_II_NAMESPACE_OPEN
namespace internal
{
namespace MatrixFreeFunctions
{
// ----------------- actual ShapeInfo functions --------------------
template <typename Number>
ShapeInfo<Number>::ShapeInfo ()
:
element_type (tensor_general),
n_q_points (0),
dofs_per_cell (0)
{}
template <typename Number>
template <int dim>
void
ShapeInfo<Number>::reinit (const Quadrature<1> &quad,
const FiniteElement<dim> &fe_in,
const unsigned int base_element_number)
{
const FiniteElement<dim> *fe = &fe_in;
fe = &fe_in.base_element(base_element_number);
Assert (fe->n_components() == 1,
ExcMessage("FEEvaluation only works for scalar finite elements."));
fe_degree = fe->degree;
const unsigned int n_dofs_1d = fe_degree+1,
n_q_points_1d = quad.size();
// renumber (this is necessary for FE_Q, for example, since there the
// vertex DoFs come first, which is incompatible with the lexicographic
// ordering necessary to apply tensor products efficiently)
std::vector<unsigned int> scalar_lexicographic;
{
// find numbering to lexicographic
Assert(fe->n_components() == 1,
ExcMessage("Expected a scalar element"));
const FE_Poly<TensorProductPolynomials<dim>,dim,dim> *fe_poly =
dynamic_cast<const FE_Poly<TensorProductPolynomials<dim>,dim,dim>*>(fe);
const FE_Poly<TensorProductPolynomials<dim,Polynomials::
PiecewisePolynomial<double> >,dim,dim> *fe_poly_piece =
dynamic_cast<const FE_Poly<TensorProductPolynomials<dim,
Polynomials::PiecewisePolynomial<double> >,dim,dim>*> (fe);
const FE_DGP<dim> *fe_dgp = dynamic_cast<const FE_DGP<dim>*>(fe);
const FE_Q_DG0<dim> *fe_q_dg0 = dynamic_cast<const FE_Q_DG0<dim>*>(fe);
element_type = tensor_general;
if (fe_poly != 0)
scalar_lexicographic = fe_poly->get_poly_space_numbering_inverse();
else if (fe_poly_piece != 0)
scalar_lexicographic = fe_poly_piece->get_poly_space_numbering_inverse();
else if (fe_dgp != 0)
{
scalar_lexicographic.resize(fe_dgp->dofs_per_cell);
for (unsigned int i=0; i<fe_dgp->dofs_per_cell; ++i)
scalar_lexicographic[i] = i;
element_type = truncated_tensor;
}
else if (fe_q_dg0 != 0)
{
scalar_lexicographic = fe_q_dg0->get_poly_space_numbering_inverse();
element_type = tensor_symmetric_plus_dg0;
}
else
Assert(false, ExcNotImplemented());
// Finally store the renumbering into the member variable of this
// class
if (fe_in.n_components() == 1)
lexicographic_numbering = scalar_lexicographic;
else
{
// have more than one component, get the inverse
// permutation, invert it, sort the components one after one,
// and invert back
std::vector<unsigned int> scalar_inv =
Utilities::invert_permutation(scalar_lexicographic);
std::vector<unsigned int> lexicographic(fe_in.dofs_per_cell,
numbers::invalid_unsigned_int);
unsigned int components_before = 0;
for (unsigned int e=0; e<base_element_number; ++e)
components_before += fe_in.element_multiplicity(e);
for (unsigned int comp=0;
comp<fe_in.element_multiplicity(base_element_number); ++comp)
for (unsigned int i=0; i<scalar_inv.size(); ++i)
lexicographic[fe_in.component_to_system_index(comp+components_before,i)]
= scalar_inv.size () * comp + scalar_inv[i];
// invert numbering again. Need to do it manually because we might
// have undefined blocks
lexicographic_numbering.resize(fe_in.element_multiplicity(base_element_number)*fe->dofs_per_cell);
for (unsigned int i=0; i<lexicographic.size(); ++i)
if (lexicographic[i] != numbers::invalid_unsigned_int)
{
AssertIndexRange(lexicographic[i],
lexicographic_numbering.size());
lexicographic_numbering[lexicographic[i]] = i;
}
}
// to evaluate 1D polynomials, evaluate along the line where y=z=0,
// assuming that shape_value(0,Point<dim>()) == 1. otherwise, need
// other entry point (e.g. generating a 1D element by reading the
// name, as done before r29356)
Assert(std::fabs(fe->shape_value(scalar_lexicographic[0],
Point<dim>())-1) < 1e-13,
ExcInternalError());
}
n_q_points = Utilities::fixed_power<dim>(n_q_points_1d);
dofs_per_cell = fe->dofs_per_cell;
n_q_points_face = dim>1?Utilities::fixed_power<dim-1>(n_q_points_1d):1;
dofs_per_face = fe->dofs_per_face;
const unsigned int array_size = n_dofs_1d*n_q_points_1d;
this->shape_gradients.resize_fast (array_size);
this->shape_values.resize_fast (array_size);
this->shape_hessians.resize_fast (array_size);
this->face_value[0].resize(n_dofs_1d);
this->face_gradient[0].resize(n_dofs_1d);
this->subface_value[0].resize(array_size);
this->face_value[1].resize(n_dofs_1d);
this->face_gradient[1].resize(n_dofs_1d);
this->subface_value[1].resize(array_size);
this->shape_values_number.resize (array_size);
this->shape_gradient_number.resize (array_size);
for (unsigned int i=0; i<n_dofs_1d; ++i)
{
// need to reorder from hierarchical to lexicographic to get the
// DoFs correct
const unsigned int my_i = scalar_lexicographic[i];
for (unsigned int q=0; q<n_q_points_1d; ++q)
{
// fill both vectors with
// VectorizedArray<Number>::n_array_elements
// copies for the shape information and
// non-vectorized fields
Point<dim> q_point;
q_point[0] = quad.get_points()[q][0];
shape_values_number[i*n_q_points_1d+q] = fe->shape_value(my_i,q_point);
shape_gradient_number[i*n_q_points_1d+q] = fe->shape_grad (my_i,q_point)[0];
shape_values [i*n_q_points_1d+q] =
shape_values_number [i*n_q_points_1d+q];
shape_gradients[i*n_q_points_1d+q] =
shape_gradient_number[i*n_q_points_1d+q];
shape_hessians[i*n_q_points_1d+q] =
fe->shape_grad_grad(my_i,q_point)[0][0];
q_point[0] *= 0.5;
subface_value[0][i*n_q_points_1d+q] = fe->shape_value(my_i,q_point);
q_point[0] += 0.5;
subface_value[1][i*n_q_points_1d+q] = fe->shape_value(my_i,q_point);
}
Point<dim> q_point;
this->face_value[0][i] = fe->shape_value(my_i,q_point);
this->face_gradient[0][i] = fe->shape_grad(my_i,q_point)[0];
q_point[0] = 1;
this->face_value[1][i] = fe->shape_value(my_i,q_point);
this->face_gradient[1][i] = fe->shape_grad(my_i,q_point)[0];
}
if (element_type == tensor_general &&
check_1d_shapes_symmetric(n_q_points_1d))
{
if (check_1d_shapes_gausslobatto())
element_type = tensor_gausslobatto;
else
element_type = tensor_symmetric;
}
else if (element_type == tensor_symmetric_plus_dg0)
check_1d_shapes_symmetric(n_q_points_1d);
// face information
unsigned int n_faces = GeometryInfo<dim>::faces_per_cell;
this->face_indices.reinit(n_faces, this->dofs_per_face);
switch (dim)
{
case 3:
{
for (unsigned int i=0; i<this->dofs_per_face; i++)
{
const unsigned int jump_term =
this->dofs_per_face*((i*n_dofs_1d)/this->dofs_per_face);
this->face_indices(0,i) = i*n_dofs_1d;
this->face_indices(1,i) = i*n_dofs_1d + n_dofs_1d-1;
this->face_indices(2,i) = i%n_dofs_1d + jump_term;
this->face_indices(3,i) = (i%n_dofs_1d + jump_term +
(n_dofs_1d-1)*n_dofs_1d);
this->face_indices(4,i) = i;
this->face_indices(5,i) = (n_dofs_1d-1)*this->dofs_per_face+i;
}
break;
}
case 2:
{
for (unsigned int i=0; i<this->dofs_per_face; i++)
{
this->face_indices(0,i) = n_dofs_1d*i;
this->face_indices(1,i) = n_dofs_1d*i + n_dofs_1d-1;
this->face_indices(2,i) = i;
this->face_indices(3,i) = (n_dofs_1d-1)*n_dofs_1d+i;
}
break;
}
case 1:
{
this->face_indices(0,0) = 0;
this->face_indices(1,0) = n_dofs_1d-1;
break;
}
default:
Assert (false, ExcNotImplemented());
}
}
template <typename Number>
bool
ShapeInfo<Number>::check_1d_shapes_symmetric(const unsigned int n_q_points_1d)
{
const double zero_tol =
types_are_equal<Number,double>::value==true?1e-10:1e-7;
// symmetry for values
const unsigned int n_dofs_1d = fe_degree + 1;
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
if (std::fabs(shape_values[i*n_q_points_1d+j][0] -
shape_values[(n_dofs_1d-i)*n_q_points_1d
-j-1][0]) > zero_tol)
return false;
// shape values should be zero at x=0.5 for all basis functions except
// for one which is one
if (n_q_points_1d%2 == 1 && n_dofs_1d%2 == 1)
{
for (unsigned int i=0; i<n_dofs_1d/2; ++i)
if (std::fabs(shape_values[i*n_q_points_1d+
n_q_points_1d/2][0]) > zero_tol)
return false;
if (std::fabs(shape_values[(n_dofs_1d/2)*n_q_points_1d+
n_q_points_1d/2][0]-1.)> zero_tol)
return false;
}
// skew-symmetry for gradient, zero of middle basis function in middle
// quadrature point
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
if (std::fabs(shape_gradients[i*n_q_points_1d+j][0] +
shape_gradients[(n_dofs_1d-i)*n_q_points_1d-
j-1][0]) > zero_tol)
return false;
if (n_dofs_1d%2 == 1 && n_q_points_1d%2 == 1)
if (std::fabs(shape_gradients[(n_dofs_1d/2)*n_q_points_1d+
(n_q_points_1d/2)][0]) > zero_tol)
return false;
// symmetry for Laplacian
for (unsigned int i=0; i<(n_dofs_1d+1)/2; ++i)
for (unsigned int j=0; j<n_q_points_1d; ++j)
if (std::fabs(shape_hessians[i*n_q_points_1d+j][0] -
shape_hessians[(n_dofs_1d-i)*n_q_points_1d-
j-1][0]) > zero_tol)
return false;
const unsigned int stride = (n_q_points_1d+1)/2;
shape_val_evenodd.resize((fe_degree+1)*stride);
shape_gra_evenodd.resize((fe_degree+1)*stride);
shape_hes_evenodd.resize((fe_degree+1)*stride);
for (unsigned int i=0; i<(fe_degree+1)/2; ++i)
for (unsigned int q=0; q<stride; ++q)
{
shape_val_evenodd[i*stride+q] =
Number(0.5) * (shape_values[i*n_q_points_1d+q] +
shape_values[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_val_evenodd[(fe_degree-i)*stride+q] =
Number(0.5) * (shape_values[i*n_q_points_1d+q] -
shape_values[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_gra_evenodd[i*stride+q] =
Number(0.5) * (shape_gradients[i*n_q_points_1d+q] +
shape_gradients[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_gra_evenodd[(fe_degree-i)*stride+q] =
Number(0.5) * (shape_gradients[i*n_q_points_1d+q] -
shape_gradients[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_hes_evenodd[i*stride+q] =
Number(0.5) * (shape_hessians[i*n_q_points_1d+q] +
shape_hessians[i*n_q_points_1d+n_q_points_1d-1-q]);
shape_hes_evenodd[(fe_degree-i)*stride+q] =
Number(0.5) * (shape_hessians[i*n_q_points_1d+q] -
shape_hessians[i*n_q_points_1d+n_q_points_1d-1-q]);
}
if (fe_degree % 2 == 0)
for (unsigned int q=0; q<stride; ++q)
{
shape_val_evenodd[fe_degree/2*stride+q] =
shape_values[(fe_degree/2)*n_q_points_1d+q];
shape_gra_evenodd[fe_degree/2*stride+q] =
shape_gradients[(fe_degree/2)*n_q_points_1d+q];
shape_hes_evenodd[fe_degree/2*stride+q] =
shape_hessians[(fe_degree/2)*n_q_points_1d+q];
}
return true;
}
template <typename Number>
bool
ShapeInfo<Number>::check_1d_shapes_gausslobatto()
{
if (dofs_per_cell != n_q_points)
return false;
const double zero_tol =
types_are_equal<Number,double>::value==true?1e-10:1e-7;
// check: - identity operation for shape values
// - zero diagonal at interior points for gradients
// - gradient equal to unity at element boundary
const unsigned int n_points_1d = fe_degree+1;
for (unsigned int i=0; i<n_points_1d; ++i)
for (unsigned int j=0; j<n_points_1d; ++j)
if (i!=j)
{
if (std::fabs(shape_values[i*n_points_1d+j][0])>zero_tol)
return false;
}
else
{
if (std::fabs(shape_values[i*n_points_1d+
j][0]-1.)>zero_tol)
return false;
}
for (unsigned int i=1; i<n_points_1d-1; ++i)
if (std::fabs(shape_gradients[i*n_points_1d+i][0])>zero_tol)
return false;
if (std::fabs(shape_gradients[n_points_1d-1][0]-
(n_points_1d%2==0 ? -1. : 1.)) > zero_tol)
return false;
return true;
}
template <typename Number>
std::size_t
ShapeInfo<Number>::memory_consumption () const
{
std::size_t memory = sizeof(*this);
memory += MemoryConsumption::memory_consumption(shape_values);
memory += MemoryConsumption::memory_consumption(shape_gradients);
memory += MemoryConsumption::memory_consumption(shape_hessians);
memory += MemoryConsumption::memory_consumption(shape_val_evenodd);
memory += MemoryConsumption::memory_consumption(shape_gra_evenodd);
memory += MemoryConsumption::memory_consumption(shape_hes_evenodd);
memory += face_indices.memory_consumption();
for (unsigned int i=0; i<2; ++i)
{
memory += MemoryConsumption::memory_consumption(face_value[i]);
memory += MemoryConsumption::memory_consumption(face_gradient[i]);
}
memory += MemoryConsumption::memory_consumption(shape_values_number);
memory += MemoryConsumption::memory_consumption(shape_gradient_number);
return memory;
}
// end of functions for ShapeInfo
} // end of namespace MatrixFreeFunctions
} // end of namespace internal
DEAL_II_NAMESPACE_CLOSE
|