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CGGTonsorialBubbleBase.cpp
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1/** \file CGGTonsorialBubbleBase.hpp
2
3 \brief Implementation of tonsorial bubble base div(v) = 0.
4
5 Implementation is based and motiveted by \cite cockburn2010new. This base
6 is used to approximate stresses using Hdiv base with weakly enforced
7 symmetry.
8
9*/
10
11#include <MoFEM.hpp>
12#include <h1_hdiv_hcurl_l2.h>
13using namespace MoFEM;
15
16using namespace FTensor;
17
18namespace EshelbianPlasticity {
19
20MoFEMErrorCode CGG_BubbleBase_MBTET(const int p, const double *N,
21 const double *diffN,
22 Tensor2<PackPtr<double *, 9>, 3, 3> &t_phi,
23 const int gdim) {
25
26 // FIXME: In this implementation symmetry of mix derivatives is not exploited
27
28 if (p < 1)
30
36
37 Tensor1<double, 3> t_diff_n[4];
38 {
39 Tensor1<PackPtr<const double *, 3>, 3> t_diff_n_tmp(&diffN[0], &diffN[1],
40 &diffN[2]);
41 for (int ii = 0; ii != 4; ++ii) {
42 t_diff_n[ii](i) = t_diff_n_tmp(i);
43 ++t_diff_n_tmp;
44 }
45 }
46
47 Tensor1<double, 3> t_diff_ksi[3];
48 for (int ii = 0; ii != 3; ++ii)
49 t_diff_ksi[ii](i) = t_diff_n[ii + 1](i) - t_diff_n[0](i);
50
51 int lp = p >= 2 ? p - 2 + 1 : 0;
52 VectorDouble l[3] = {VectorDouble(lp + 1), VectorDouble(lp + 1),
53 VectorDouble(lp + 1)};
54 MatrixDouble diff_l[3] = {MatrixDouble(3, lp + 1), MatrixDouble(3, lp + 1),
55 MatrixDouble(3, lp + 1)};
56 MatrixDouble diff2_l[3] = {MatrixDouble(9, lp + 1), MatrixDouble(9, lp + 1),
57 MatrixDouble(9, lp + 1)};
58
59 for (int ii = 0; ii != 3; ++ii)
60 diff2_l[ii].clear();
61
62 for (int gg = 0; gg != gdim; ++gg) {
63
64 const int node_shift = gg * 4;
65
66 for (int ii = 0; ii != 3; ++ii) {
67
68 auto &t_diff_ksi_ii = t_diff_ksi[ii];
69 auto &l_ii = l[ii];
70 auto &diff_l_ii = diff_l[ii];
71 auto &diff2_l_ii = diff2_l[ii];
72
73 double ksi_ii = N[node_shift + ii + 1] - N[node_shift + 0];
74
75 CHKERR Legendre_polynomials(lp, ksi_ii, &t_diff_ksi_ii(0),
76 &*l_ii.data().begin(),
77 &*diff_l_ii.data().begin(), 3);
78
79 for (int l = 1; l < lp; ++l) {
80 const double a = ((2 * (double)l + 1) / ((double)l + 1));
81 const double b = ((double)l / ((double)l + 1));
82 for (int d0 = 0; d0 != 3; ++d0)
83 for (int d1 = 0; d1 != 3; ++d1) {
84 const int r = 3 * d0 + d1;
85 diff2_l_ii(r, l + 1) = a * (t_diff_ksi_ii(d0) * diff_l_ii(d1, l) +
86 t_diff_ksi_ii(d1) * diff_l_ii(d0, l) +
87 ksi_ii * diff2_l_ii(r, l)) -
88 b * diff2_l_ii(r, l - 1);
89 }
90 }
91 }
92
93 const double n[] = {N[node_shift + 0], N[node_shift + 1], N[node_shift + 2],
94 N[node_shift + 3]};
95
98 const int tab[4][4] = {
99 {1, 2, 3, 0}, {2, 3, 0, 1}, {3, 0, 1, 2}, {0, 1, 2, 3}};
100 t_bk(i, j) = 0;
101 t_bk_diff(i, j, k) = 0;
102 for (int ii = 0; ii != 3; ++ii) {
103 const int i0 = tab[ii][0];
104 const int i1 = tab[ii][1];
105 const int i2 = tab[ii][2];
106 const int i3 = tab[ii][3];
107 auto &t_diff_n_i0 = t_diff_n[i0];
108 auto &t_diff_n_i1 = t_diff_n[i1];
109 auto &t_diff_n_i2 = t_diff_n[i2];
110 auto &t_diff_n_i3 = t_diff_n[i3];
112 t_k(i, j) = t_diff_n_i3(i) * t_diff_n_i3(j);
113 const double b = n[i0] * n[i1] * n[i2];
114 t_bk(i, j) += b * t_k(i, j);
115 Tensor1<double, 3> t_diff_b;
116 t_diff_b(i) = t_diff_n_i0(i) * n[i1] * n[i2] +
117 t_diff_n_i1(i) * n[i0] * n[i2] +
118 t_diff_n_i2(i) * n[i0] * n[i1];
119 t_bk_diff(i, j, k) += t_k(i, j) * t_diff_b(k);
120 }
121
122 int zz = 0;
123 for (int o = p - 2 + 1; o <= p - 2 + 1; ++o) {
124
125 for (int ii = 0; ii <= o; ++ii)
126 for (int jj = 0; (ii + jj) <= o; ++jj) {
127
128 const int kk = o - ii - jj;
129
130 auto get_diff_l = [&](const int y, const int i) {
131 return Tensor1<double, 3>(diff_l[y](0, i), diff_l[y](1, i),
132 diff_l[y](2, i));
133 };
134 auto get_diff2_l = [&](const int y, const int i) {
136 diff2_l[y](0, i), diff2_l[y](1, i), diff2_l[y](2, i),
137 diff2_l[y](3, i), diff2_l[y](4, i), diff2_l[y](5, i),
138 diff2_l[y](6, i), diff2_l[y](7, i), diff2_l[y](8, i));
139 };
140
141 auto l_i = l[0][ii];
142 auto t_diff_i = get_diff_l(0, ii);
143 auto t_diff2_i = get_diff2_l(0, ii);
144 auto l_j = l[1][jj];
145 auto t_diff_j = get_diff_l(1, jj);
146 auto t_diff2_j = get_diff2_l(1, jj);
147 auto l_k = l[2][kk];
148 auto t_diff_k = get_diff_l(2, kk);
149 auto t_diff2_k = get_diff2_l(2, kk);
150
151 Tensor1<double, 3> t_diff_l2;
152 t_diff_l2(i) = t_diff_i(i) * l_j * l_k + t_diff_j(i) * l_i * l_k +
153 t_diff_k(i) * l_i * l_j;
154 Tensor2<double, 3, 3> t_diff2_l2;
155 t_diff2_l2(i, j) =
156 t_diff2_i(i, j) * l_j * l_k + t_diff_i(i) * t_diff_j(j) * l_k +
157 t_diff_i(i) * l_j * t_diff_k(j) +
158
159 t_diff2_j(i, j) * l_i * l_k + t_diff_j(i) * t_diff_i(j) * l_k +
160 t_diff_j(i) * l_i * t_diff_k(j) +
161
162 t_diff2_k(i, j) * l_i * l_j + t_diff_k(i) * t_diff_i(j) * l_j +
163 t_diff_k(i) * l_i * t_diff_j(j);
164
165 for (int dd = 0; dd != 3; ++dd) {
166
167 Tensor2<double, 3, 3> t_axial_diff;
168 t_axial_diff(i, j) = 0;
169 for (int mm = 0; mm != 3; ++mm)
170 t_axial_diff(dd, mm) = t_diff_l2(mm);
171
173 t_A_diff(i, j, k) = levi_civita(i, j, m) * t_axial_diff(m, k);
174 Tensor2<double, 3, 3> t_curl_A;
175 t_curl_A(i, j) = levi_civita(j, m, f) * t_A_diff(i, f, m);
176 Tensor3<double, 3, 3, 3> t_curl_A_bK_diff;
177 t_curl_A_bK_diff(i, j, k) = t_curl_A(i, m) * t_bk_diff(m, j, k);
178
179 Tensor3<double, 3, 3, 3> t_axial_diff2;
180 t_axial_diff2(i, j, k) = 0;
181 for (int mm = 0; mm != 3; ++mm)
182 for (int nn = 0; nn != 3; ++nn)
183 t_axial_diff2(dd, mm, nn) = t_diff2_l2(mm, nn);
185 t_A_diff2(i, j, k, f) =
186 levi_civita(i, j, m) * t_axial_diff2(m, k, f);
187 Tensor3<double, 3, 3, 3> t_curl_A_diff2;
188 t_curl_A_diff2(i, j, k) =
189 levi_civita(j, m, f) * t_A_diff2(i, f, m, k);
190 Tensor3<double, 3, 3, 3> t_curl_A_diff2_bK;
191 t_curl_A_diff2_bK(i, j, k) = t_curl_A_diff2(i, m, k) * t_bk(m, j);
192
193 t_phi(i, j) = levi_civita(j, m, f) * (t_curl_A_bK_diff(i, f, m) +
194 t_curl_A_diff2_bK(i, f, m));
195
196 ++t_phi;
197 ++zz;
198 }
199 }
200 }
201 if (zz != NBVOLUMETET_CCG_BUBBLE(p))
202 SETERRQ2(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
203 "Wrong number of base functions %d != %d", zz,
205 }
206
208}
209
210} // namespace EshelbianPlasticity
static Index< 'o', 3 > o
static Index< 'p', 3 > p
Implementation of tonsorial bubble base div(v) = 0.
#define NBVOLUMETET_CCG_BUBBLE(P)
Bubble function for CGG H div space.
constexpr double a
#define MoFEMFunctionReturnHot(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:447
@ MOFEM_DATA_INCONSISTENCY
Definition: definitions.h:31
#define CHKERR
Inline error check.
Definition: definitions.h:535
#define MoFEMFunctionBeginHot
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:440
FTensor::Index< 'n', SPACE_DIM > n
FTensor::Index< 'm', SPACE_DIM > m
PetscErrorCode Legendre_polynomials(int p, double s, double *diff_s, double *L, double *diffL, const int dim)
Calculate Legendre approximation basis.
Functions to approximate hierarchical spaces.
FTensor::Index< 'i', SPACE_DIM > i
FTensor::Index< 'l', 3 > l
FTensor::Index< 'j', 3 > j
FTensor::Index< 'k', 3 > k
MoFEMErrorCode CGG_BubbleBase_MBTET(const int p, const double *N, const double *diffN, FTensor::Tensor2< FTensor::PackPtr< double *, 9 >, 3, 3 > &phi, const int gdim)
Calculate CGGT tonsorial bubble base.
Tensors class implemented by Walter Landry.
Definition: FTensor.hpp:51
constexpr std::enable_if<(Dim0<=2 &&Dim1<=2), Tensor2_Expr< Levi_Civita< T >, T, Dim0, Dim1, i, j > >::type levi_civita(const Index< i, Dim0 > &, const Index< j, Dim1 > &)
levi_civita functions to make for easy adhoc use
const Tensor2_symmetric_Expr< const ddTensor0< T, Dim, i, j >, typename promote< T, double >::V, Dim, i, j > dd(const Tensor0< T * > &a, const Index< i, Dim > index1, const Index< j, Dim > index2, const Tensor1< int, Dim > &d_ijk, const Tensor1< double, Dim > &d_xyz)
Definition: ddTensor0.hpp:33
PetscErrorCode MoFEMErrorCode
MoFEM/PETSc error code.
Definition: Exceptions.hpp:56
UBlasMatrix< double > MatrixDouble
Definition: Types.hpp:77
UBlasVector< double > VectorDouble
Definition: Types.hpp:68
implementation of Data Operators for Forces and Sources
Definition: Common.hpp:10
const int N
Definition: speed_test.cpp:3