/usr/include/rheolef/piola.h is in librheolef-dev 6.7-6.
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 | #ifndef _RHEOLEF_PIOLA_H
#define _RHEOLEF_PIOLA_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//
// piola on a predefined point set: hat_x[q], q=0..nq
//
#include "rheolef/geo.h"
#include "rheolef/basis_on_pointset.h"
namespace rheolef {
template<class T, class M>
point_basic<T>
piola_transformation (
const geo_basic<T,M>& omega,
const basis_on_pointset<T>& piola_on_pointset,
reference_element hat_K,
const std::vector<size_t>& dis_inod,
size_t q);
// ------------------------------------------
// jacobian of the piola transformation
// at an aritrarily point hat_x
// ------------------------------------------
template<class T, class M>
void
jacobian_piola_transformation (
const geo_basic<T,M>& omega,
const basis_on_pointset<T>& piola_on_pointset,
reference_element hat_K,
const std::vector<size_t>& dis_inod,
const point_basic<T>& hat_x,
tensor_basic<T>& DF);
// ------------------------------------------
// jacobian of the piola transformation
// at a quadrature point
// ------------------------------------------
template<class T, class M>
void
jacobian_piola_transformation (
const geo_basic<T,M>& omega,
const basis_on_pointset<T>& piola_on_pointset,
reference_element hat_K,
const std::vector<size_t>& dis_inod,
size_t q,
tensor_basic<T>& DF);
template <class T>
T
det_jacobian_piola_transformation (const tensor_basic<T>& DF, size_t d , size_t map_d);
// The pseudo inverse extend inv(DF) for face in 3d or edge in 2d
// i.e. usefull for Laplacian-Beltrami and others surfacic forms.
//
// pinvDF (hat_xq) = inv DF, if tetra in 3d, tri in 2d, etc
// = pseudo-invese, when tri in 3d, edge in 2 or 3d
// e.g. on 3d face : pinvDF*DF = [1, 0, 0; 0, 1, 0; 0, 0, 0]
//
// let DF = [u, v, w], where u, v, w are the column vectors of DF
// then det(DF) = mixt(u,v,w)
// and det(DF)*inv(DF)^T = [v^w, w^u, u^v] where u^v = vect(u,v)
//
// application:
// if K=triangle(a,b,c) then u=ab=b-a, v=ac=c-a and w = n = u^v/|u^v|.
// Thus DF = [ab,ac,n] and det(DF)=|ab^ac|
// and inv(DF)^T = [ac^n/|ab^ac|, -ab^n/|ab^ac|, n]
// The pseudo-inverse is obtained by remplacing the last column n by zero.
//
template<class T, class M>
point_basic<T>
normal_from_piola_transformation (const geo_basic<T,M>& omega, const geo_element& S, const tensor_basic<T>& DF, size_t d);
// The pseudo inverse extend inv(DF) for face in 3d or edge in 2d
// i.e. usefull for Laplacian-Beltrami and others surfacic forms.
//
// pinvDF (hat_xq) = inv DF, if tetra in 3d, tri in 2d, etc
// = pseudo-invese, when tri in 3d, edge in 2 or 3d
// e.g. on 3d face : pinvDF*DF = [1, 0, 0; 0, 1, 0; 0, 0, 0]
//
// let DF = [u, v, w], where u, v, w are the column vectors of DF
// then det(DF) = mixt(u,v,w)
// and det(DF)*inv(DF)^T = [v^w, w^u, u^v] where u^v = vect(u,v)
//
// application:
// if K=triangle(a,b,c) then u=ab=b-a, v=ac=c-a and w = n = u^v/|u^v|.
// Thus DF = [ab,ac,n] and det(DF)=|ab^ac|
// and inv(DF)^T = [ac^n/|ab^ac|, -ab^n/|ab^ac|, n]
// The pseudo-inverse is obtained by remplacing the last column n by zero.
//
template<class T>
tensor_basic<T>
pseudo_inverse_jacobian_piola_transformation (
const tensor_basic<T>& DF,
size_t d,
size_t map_d);
// DF: hat_x --> DF(hat_x) on hat_K
template<class T, class M>
void
jacobian_piola_transformation (
const geo_basic<T,M>& omega,
reference_element hat_K,
const std::vector<size_t>& dis_inod,
const point_basic<T>& hat_x,
tensor_basic<T>& DF);
// F^{-1}: x --> hat_x on K
template<class T, class M>
point_basic<T>
inverse_piola_transformation (
const geo_basic<T,M>& omega,
const reference_element& hat_K,
const std::vector<size_t>& dis_inod,
const point_basic<T>& x);
// compute: P = I - nxn, the tangential projector on a map with unit normal n
template <class T>
void map_projector (const tensor_basic<T>& DF, size_t d, size_t map_d, tensor_basic<T>& P);
// axisymetric weight ?
// point_basic<T> xq = rheolef::piola_transformation (_omega, _piola_table, K, dis_inod, q);
template<class T>
T
weight_coordinate_system (space_constant::coordinate_type sys_coord, const point_basic<T>& xq);
template<class T, class M>
T
weight_coordinate_system (
const geo_basic<T,M>& omega,
const basis_on_pointset<T>& piola_table,
const geo_element& K,
const std::vector<size_t>& dis_inod,
size_t q);
}// namespace rheolef
#endif // _RHEOLEF_PIOLA_H
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