v0.8.23
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>
13 using namespace MoFEM;
15 
16 using namespace FTensor;
17 
18 namespace EshelbianPlasticity {
19 
20 MoFEMErrorCode 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 
31  Index<'i', 3> i;
32  Index<'j', 3> j;
34  Index<'m', 3> m;
35  Index<'f', 3> f;
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 
94  const double n[] = {N[node_shift + 0], N[node_shift + 1], N[node_shift + 2],
95  N[node_shift + 3]};
96 
98  Tensor3<double, 3, 3, 3> t_bk_diff;
99  const int tab[4][4] = {
100  {1, 2, 3, 0}, {2, 3, 0, 1}, {3, 0, 1, 2}, {0, 1, 2, 3}};
101  t_bk(i, j) = 0;
102  t_bk_diff(i, j, k) = 0;
103  for (int ii = 0; ii != 3; ++ii) {
104  const int i0 = tab[ii][0];
105  const int i1 = tab[ii][1];
106  const int i2 = tab[ii][2];
107  const int i3 = tab[ii][3];
108  auto &t_diff_n_i0 = t_diff_n[i0];
109  auto &t_diff_n_i1 = t_diff_n[i1];
110  auto &t_diff_n_i2 = t_diff_n[i2];
111  auto &t_diff_n_i3 = t_diff_n[i3];
113  t_k(i, j) = t_diff_n_i3(i) * t_diff_n_i3(j);
114  const double b = n[i0] * n[i1] * n[i2];
115  t_bk(i, j) += b * t_k(i, j);
116  Tensor1<double, 3> t_diff_b;
117  t_diff_b(i) = t_diff_n_i0(i) * n[i1] * n[i2] +
118  t_diff_n_i1(i) * n[i0] * n[i2] +
119  t_diff_n_i2(i) * n[i0] * n[i1];
120  t_bk_diff(i, j, k) += t_k(i, j) * t_diff_b(k);
121  }
122 
123  int zz = 0;
124  for (int o = p - 2 + 1; o <= p - 2 + 1; ++o) {
125 
126  for (int ii = 0; ii <= o; ++ii)
127  for (int jj = 0; (ii + jj) <= o; ++jj) {
128 
129  const int kk = o - ii - jj;
130 
131  auto get_diff_l = [&](const int y, const int i) {
132  return Tensor1<double, 3>(diff_l[y](0, i), diff_l[y](1, i),
133  diff_l[y](2, i));
134  };
135  auto get_diff2_l = [&](const int y, const int i) {
136  return Tensor2<double, 3, 3>(
137  diff2_l[y](0, i), diff2_l[y](1, i), diff2_l[y](2, i),
138  diff2_l[y](3, i), diff2_l[y](4, i), diff2_l[y](5, i),
139  diff2_l[y](6, i), diff2_l[y](7, i), diff2_l[y](8, i));
140  };
141 
142  auto l_i = l[0][ii];
143  auto t_diff_i = get_diff_l(0, ii);
144  auto t_diff2_i = get_diff2_l(0, ii);
145  auto l_j = l[1][jj];
146  auto t_diff_j = get_diff_l(1, jj);
147  auto t_diff2_j = get_diff2_l(1, jj);
148  auto l_k = l[2][kk];
149  auto t_diff_k = get_diff_l(2, kk);
150  auto t_diff2_k = get_diff2_l(2, kk);
151 
152  Tensor1<double, 3> t_diff_l2;
153  t_diff_l2(i) = t_diff_i(i) * l_j * l_k + t_diff_j(i) * l_i * l_k +
154  t_diff_k(i) * l_i * l_j;
155  Tensor2<double, 3, 3> t_diff2_l2;
156  t_diff2_l2(i, j) =
157  t_diff2_i(i, j) * l_j * l_k + t_diff_i(i) * t_diff_j(j) * l_k +
158  t_diff_i(i) * l_j * t_diff_k(j) +
159 
160  t_diff2_j(i, j) * l_i * l_k + t_diff_j(i) * t_diff_i(j) * l_k +
161  t_diff_j(i) * l_i * t_diff_k(j) +
162 
163  t_diff2_k(i, j) * l_i * l_j + t_diff_k(i) * t_diff_i(j) * l_j +
164  t_diff_k(i) * l_i * t_diff_j(j);
165 
166  for (int dd = 0; dd != 3; ++dd) {
167 
168  Tensor2<double, 3, 3> t_axial_diff;
169  t_axial_diff(i, j) = 0;
170  for (int mm = 0; mm != 3; ++mm)
171  t_axial_diff(dd, mm) = t_diff_l2(mm);
172 
173  Tensor3<double, 3, 3, 3> t_A_diff;
174  t_A_diff(i, j, k) = levi_civita(i, j, m) * t_axial_diff(m, k);
175  Tensor2<double, 3, 3> t_curl_A;
176  t_curl_A(i, j) = levi_civita(j, m, f) * t_A_diff(i, f, m);
177  Tensor3<double, 3, 3, 3> t_curl_A_bK_diff;
178  t_curl_A_bK_diff(i, j, k) = t_curl_A(i, m) * t_bk_diff(m, j, k);
179 
180  Tensor3<double, 3, 3, 3> t_axial_diff2;
181  t_axial_diff2(i, j, k) = 0;
182  for (int mm = 0; mm != 3; ++mm)
183  for (int nn = 0; nn != 3; ++nn)
184  t_axial_diff2(dd, mm, nn) = t_diff2_l2(mm, nn);
185  Tensor4<double, 3, 3, 3, 3> t_A_diff2;
186  t_A_diff2(i, j, k, f) =
187  levi_civita(i, j, m) * t_axial_diff2(m, k, f);
188  Tensor3<double, 3, 3, 3> t_curl_A_diff2;
189  t_curl_A_diff2(i, j, k) =
190  levi_civita(j, m, f) * t_A_diff2(i, f, m, k);
191  Tensor3<double, 3, 3, 3> t_curl_A_diff2_bK;
192  t_curl_A_diff2_bK(i, j, k) = t_curl_A_diff2(i, m, k) * t_bk(m, j);
193 
194  t_phi(i, j) = levi_civita(j, m, f) * (t_curl_A_bK_diff(i, f, m) +
195  t_curl_A_diff2_bK(i, f, m));
196 
197  ++t_phi;
198  ++zz;
199  }
200  }
201  }
202  if(zz != NBVOLUMETET_CCG_BUBBLE(p))
203  SETERRQ2(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
204  "Wrong number of base functions %d != %d", zz,
206 
207  }
208 
210 }
211 
212 } // namespace EshelbianPlasticity
213 
PetscErrorCode Legendre_polynomials(int p, double s, double *diff_s, double *L, double *diffL, const int dim)
Calculate Legendre approximation basis.
#define MoFEMFunctionBeginHot
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:500
ublas::matrix< double, ublas::row_major, DoubleAllocator > MatrixDouble
Definition: Types.hpp:77
#define MoFEMFunctionReturnHot(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:507
Fully Antisymmetric Levi-Civita Tensor.
implementation of Data Operators for Forces and Sources
Definition: Common.hpp:21
Implementation of tonsorial bubble base div(v) = 0.
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:66
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.
#define CHKERR
Inline error check.
Definition: definitions.h:595
Functions to approximate hierarchical spaces.
#define NBVOLUMETET_CCG_BUBBLE(P)
Bubble function for CGG H div space.
ublas::vector< double, DoubleAllocator > VectorDouble
Definition: Types.hpp:76
const int N
Definition: speed_test.cpp:3
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